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Full text of "Introduction to Radar Systems"

Introduction to 



RADAR SYSTEMS 



>21 




McC RAW-HILL 




Introduction to 

RADAR SYSTEMS 



MERRILL I. SKOLNIK 

Research Division 

Electronic Communications, Inc. 



McGRAW-HILL BOOK COMPANY, INC. 1962 
New York San Francisco Toronto London 




PRESTON 



fcZUO^ 



8381 




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^o7c5 1 °t°S <f 



INTRODUCTION TO RADAR SYSTEMS 

Copyright © 1962 by the McGraw-Hill Book Company, Inc. Printed 
in the United States of America. All rights reserved. This book, or 
parts thereof, may not be reproduced in any form without permission 
of the publishers. Library of Congress Catalog Card Number 61-17675 

57905 



PREFACE 



The subject matter of electrical engineering may be classified according to (1) com- 
ponents, (2) techniques, and (3) systems. Components are the basic building blocks 
that are combined, using the proper techniques, to yield a system. This book attempts 
to present a unified approach to the systems aspect of radar. Although the subject of 
radar systems is of particular interest to specialists in the radar field, it is also of 
interest to a much wider audience, especially the civilian and military users of radar, 
the electrical and mechanical components specialists whose devices make up a radar 
system, the operations analysts and systems engineers who must plan for employing 
radar as part of larger systems, as well as practicing engineers and scientists in related 
fields. 

This book originated in the notes for a graduate course in radar systems engineering 
taught for several years in the Graduate Evening Division of Northeastern University 
(while the author was a staff member at MIT Lincoln Laboratory) and, later, as an 
off-campus course at the Martin Co. for the Drexel Institute of Technology. Since 
most electrical engineering courses are usually concerned with either components or 
techniques, a course dealing with electronic systems (in this instance, radar systems) 
broadens the engineering background of the student by giving him the opportunity to 
apply the material learned from his components and techniques courses, as well as 
introducing him to the techniques, tools, and analytical procedures of the systems 
engineer. 

The book may be divided into four parts. Chapters 1 to 5 deal with subjects which 
are characteristic of radar per se and include a brief introduction and historical survey, 
the prediction of radar range performance, and discussions of the pulse, CW, FM-CW, 
MTI, pulse-doppler, conical-scan, and monopulse radars. 

The second part, Chapters 6 to 8, is concerned with the subsystems and major 
components constituting a radar system, such as transmitters, modulators, duplexers, 
antennas, receivers, and indicators. The emphasis is on those aspects of components 
of interest to radar. Only brief consideration is given to the operating principles of 
components. Many books are available that can provide more detailed descriptions 
than is possible in the limited space allotted here. 

The third part, Chapters 9 to 12, treats various topics of special importance to the 
radar systems engineer. These include the detection of signals in noise and the 
extraction of information from radar signals, both of which are based on modern 
communication theory and random-noise theory. This is followed by the environ- 
mental factors influencing radar design, for example, propagation, clutter, weather, 
and interference. 

The last portion of the book deals with radar systems and their application. 
Several brief examples of radars are given in Chapter 13. The book concludes with a 
chapter on the application of radar to the detection of extraterrestrial objects such as 
planets, satellites, meteors, aurora, and the moon. 

Although mathematics is a valuable tool of the systems engineer, no special mathe- 
matical background is assumed here. Where mathematics is necessary, it is reviewed 
briefly in the text. 

To attempt to treat thoroughly all aspects of a radar system, its component parts, 
and its analysis is an almost impossible task within a single volume, since the subject 



vi Preface 

of radar encompasses almost all electrical engineering. Extensive references to the 
published literature are included for those desiring more detail. 

Radar has been used on the ground, on the sea, and in the air, and undoubtedly it 
will be used in space. The environment in which a specific radar operates will have an 
important influence on its design. Although an attempt is made to be as general as 
possible, when it is necessary to particularize the radar environment, a ground-based 
radar is assumed unless otherwise stated. 

The function of the radar systems engineer is to utilize' the available components and 
techniques to evolve a system that will operate in a particular environment and satisfy 
the objectives and requirements desired by the potential user. It is hoped that this 
book will serve to aid those involved in this process. 

Merrill I. Skolnik 



CONTENTS 



CHAPTER 1. 

1.1 
1.2 
1.3 
1.4 

1.5 
1.6 



Preface 

THE NATURE OF RADAR 

Introduction 1 

The Radar Equation 3 

Radar Block Diagram and Operation 

Radar Frequencies 7 

History of Radar Development 8 

Applications of Radar 14 

References 19 



chapter 2. THE RADAR EQUATION 



20 



2.1 

2.2 

2.3 

2.4 

2.5 

2.6 

2.7 

2.8 

2.9 

2.10 

2.11 

2.12 

2.13 

2.14 



CHAPTER 3. 



3.1 

3.2 
3.3 
3.4 
3.5 



CHAPTER 4. 
4.1 

4.2 
4.3 
4.4 
4.5 
4.6 
4.7 
4.8 
4.9 



CHAPTER 5. 
5.1 

5.2 
5.3 



25 



Prediction of Range Performance 20 

Minimum Detectable Signal 21 

Receiver Noise 23 

Probability-density Functions 

Signal-to-noise Ratio 29 

Integration of Radar Pulses 

Radar Cross Section of Targets 

Cross-section Fluctuations 50 

Transmitter Power 56 

Pulse Repetition Frequency and Range Ambiguities 



35 



40 



57 



Antenna Parameters 
System Losses 61 
Propagation Effects 
Summary 67 
References 70 



58 



66 



CW AND FREQUENCY-MODULATED RADAR 

The Doppler Effect 72 
CW Radar 73 

Frequency-modulated CW Radar 86 
Airborne Doppler Navigation 103 
Multiple-frequency CW Radar 106 
References 111 



72 



MTI AND PULSE-DOPPLER RADAR 



113 



113 



151 



Moving-target-indication (MTI) Radar 

Delay Lines and Cancelers 119 

Subclutter Visibility 140 

MTI Using Range Gates and Filters 

Pulse-doppler Radar 1 53 

Noncoherent MTI 154 

MTI from a Moving Platform— AMTI 155 

Fluctuations Caused by Platform Motion 157 

Effect of Sidelobes on Pulse-doppler AMTI Radar 

References 162 

TRACKING RADAR 

Tracking with Radar 164 
Sequential Lobing 165 
Conical Scan 1 66 

vii 



159 



164 



V1U 



Contents 



5.4 Simultaneous Lobing or Monopulse 175 

5.5 Target-reflection Characteristics and Angular Accuracy 

5.6 Tracking in Range 189 

5.7 Tracking in Doppler 190 

5.8 Acquisition 190 

5.9 Examples of Tracking Radars 192 

5.10 Comparison of Trackers 195 
References 196 



184 



CHAPTER 6. 
6.1 

6.2 
6.3 
6.4 
6.5 
6.6 
6.7 
6.8 



CHAPTER 7. 
7.1 

7.2 

7.3 

7.4 

7.5 

7.6 

7.7 

7.8 

7.9 

7.10 

7.11 

7.12 

7.13 



CHAPTER 8. 
8.1 

8.2 

8.3 

8.4 

8.5 

8.6 

8.7 

8.8 

8.9 

8.10 

8.11 



RADAR TRANSMITTERS 

Introduction 198 
Magnetron Oscillator 199 
Klystron Amplifier 216 
Traveling-wave-tube Amplifier 225 
Amplitron and Stabilitron 227 
Grid-controlled Tubes 233 
Comparison of Tubes 244 
Modulators 248 
References 255 

ANTENNAS 

Antenna Parameters 260 

Antenna Radiation Pattern and Aperture Distribution 264 

Parabolic-reflector Antennas 269 

Scanning-feed Reflector Antennas 277 

Cassegrain Antenna 282 

Lens Antennas 286 

Array Antennas 294 

Pattern Synthesis 320 

Cosecant-squared Antenna Pattern 329 

Effect of Broadband Signals on Antenna Patterns 330 

Effect of Errors on Radiation Patterns 336 

Radomes 343 

Focused Antennas 347 

References 349 

RECEIVERS 

The Radar Receiver 356 

Superheterodyne Receiver 357 

Receiver Noise 361 

Noise Figure 363 

Effective Noise Temperature 365 

Environmental Noise 366 

RF Amplifiers 373 

Crystal Mixers 385 

IF Amplifiers 388 

Displays 391 

Dup lexers 395 

References 403 



198 



260 



356 



chapter 9. DETECTION OF RADAR SIGNALS IN NOISE 

9.1 Introduction 408 

9.2 Matched-filter Receiver 409 

9.3 Correlation Detection 418 

9.4 Detection Criteria 422 

9.5 Inverse Probability 427 

9.6 Detector Characteristics 430 

9.7 Performance of the Radar Operator 439 

9.8 Delay-line Integrators 445 

9.9 Binary Integration 446 
References 449 



408 



Contents 



IX 



chapter 10. EXTRACTION OF INFORMATION FROM RADAR SIGNALS 



453 



10.1 
10.2 
10.3 
10.4 
10.5 
10.6 
10.7 
10.8 
10.9 

CHAPTER 11. 

11.1 
11.2 
11.3 
11.4 

11.5 
11.6 
11.7 
11.8 
11.9 



12.1 
12.2 
12.3 
12.4 
12.5 
12.6 
12.7 
12.8 
12.9 
12.10 

CHAPTER 13. 
13.1 

13.2 
13.3 
13.4 
13.5 
13.6 
13.7 

CHAPTER 14. 
14.1 

14.2 
14.3 
14.4 
14.5 
14.6 
14.7 
14.8 



Introduction 453 

Phase and Amplitude Measurements 453 

Review of Radar Measurements 455 

Statistical Estimation of Parameters — Likelihood Function 461 

Theoretical Accuracy of Range and Doppler-velocity Measurements 

Uncertainty Relation 474 

Angular Accuracy 476 

Transmitted Waveform 482 

Pulse Compression 493 

References 498 

PROPAGATION OF RADAR WAVES 

Introduction 501 

Propagation over a Plane Earth 501 

The Round Earth 506 

Refraction 506 

Anomalous Propagation 509 

Low-altitude Coverage 512 

Radar Diffraction Screen 516 

Attenuation by Atmospheric Gases 517 

Microwave-radiation Hazards 518 

References 519 



462 



501 



chapter 12. CLUTTER, WEATHER, AND INTERFERENCE 



521 



521 



545 



572 



Introduction 

Ground Clutter 522 

Sea Clutter 527 

Clutter Reduction 534 

Meteorological Echoes 539 

Attenuation by Precipitation 543 

Visibility of Targets in Weather Clutter 

Angels 551 

Interference 554 

ECM and ECCM 559 

References 567 

SYSTEMS ENGINEERING AND DESIGN 

Systems Engineering 570 
Radar Parameter Selection 571 
Example — Aircraft-surveillance Radar 
ASDE 579 

Airborne Weather-avoidance Radar 
Bistatic Radar 585 
Radar Beacons 594 
References 601 

RADAR DETECTION OF EXTRATERRESTRIAL OBJECTS 

Introduction 603 

Radar Echoes from the Moon 604 

Radar Echoes from the Planets 610 

Radar Detection of the Sun 618 

Radar Detection of Meteors 619 

Radar Observation of Auroras 621 

Radar Observation of Ionized Media 624 

Detection and Tracking of Earth Satellites and Space Vehicles 

References 634 

Index 637 



570 



582 



603 



628 



1 



THE NATURE OF RADAR 



1.1. Introduction 

Radar is an electronic device for the detection and location of objects. It operates 
by transmitting a particular type of waveform, a pulse-modulated sine wave for example, 
and detects the nature of the echo signal. Radar is used to extend the capability of 
man's senses for observing his environment, especially the sense of vision. The value 
of radar lies not in being a substitute for the eye, but in doing what the eye cannot do. 
Radar cannot resolve detail as well as the eye, nor is it yet capable of recognizing the 
"color" of objects to the degree of sophistication of which the eye is capable. How- 
ever, radar can be designed to see through those conditions impervious to normal 
human vision, such as darkness, haze, fog, rain, and snow. In addition, radar has the 
advantage of being able to measure the distance or range to the object. This is probably 
its most important attribute. 

Radar 




Antenna 
Fig. 1.1. Block diagram of an elementary form of radar. 

An elementary form of radar, shown in Fig. 1.1, consists of a transmitting antenna 
emitting electromagnetic radiation generated by an oscillator of some sort, a receiving 
antenna, and an energy-detecting device, or receiver. A portion of the transmitted 
signal is intercepted by a reflecting object (target) and is reradiated in all directions. 
It is the energy reradiated in back direction that is of prime interest to the radar. The 
receiving antenna collects the returned energy and delivers it to a receiver, where it is 
processed to detect the presence of the target and to extract its location and relative 
velocity. The distance to the target is determined by measuring the time taken for the 
radar signal to travel to the target and back. The direction, or angular position, of the 
target may be determined from the direction of arrival of the reflected wavefront. The 
usual method of measuring the direction of arrival is with narrow antenna beams. If 
relative motion exists between target and radar, the shift in the carrier frequency of the 
reflected wave (doppler effect) is a measure of the target's relative (radial) velocity and 
may be used to distinguish moving targets from stationary objects. In radars which 
continuously track the movement of a target, a continuous indication of the rate of 
change of target position is also available. 

The name radar reflects the emphasis placed by the early experimenters on a device to 
detect the presence of a target and measure its range. Radar is a contraction of the 
words radio detection and ranging. It was first developed as a detection device to warn 
of the approach of hostile aircraft and for directing antiaircraft weapons. Although a 
well-designed modern radar can usually extract more information from the target 

1 



2 Introduction to Radar Systems [Sec. 1.1 

signal than merely range, the measurement of range is still one of radar's most important 
functions. There seem to be no other competitive techniques which can measure 
range as well or as rapidly as can a radar. 

Radar was the code word officially adopted by the United States Navy in November, 
1940, as the designation for what had previously been called, among other things' 
radio echo equipment. The United States Army Signal Corps, which also did pioneer 
work in radar development, used the term radio position finding until it too adopted the 
name radar in 1942. The following year radar was substituted by the British for their 
own term RDF. The origin of the R is obscure, but DF is supposed to stand for 
direction finding, which was purposely chosen to hide the fact that a range-measuring 
device was under development. Shortly after the term was coined, however, means 
were devised for also determining the angular position, so that RDF almost immediately 
lost some of its usefulness as a code name. In France, radar was known as DEM 
{detection electromagnetique), and in Germany it was called Funkmessgerat. It is now 
almost universally called radar. 

The most common radar waveform is a train of narrow pulses modulating a sine- 
wave carrier. Although the pulse is normally rectangular in shape, it need not be, and 
could be one of many possible shapes. The distance, or range,f to the target is deter- 
mined by measuring the time taken by the pulse to travel to the target and return. 
Since electromagnetic energy travels at the speed of light, the range R is 



cAt 
* = — (l.D 



The velocity of light c is 3 x 10 8 m/sec, if R is measured in meters and A?, the time 
duration for the wave to travel out and back, is measured in seconds. One micro- 
second of round-trip travel time corresponds to a distance of 0.081 nautical mile, 
0.093 statute mile, 1 64 yd, or 492 ft. The accepted unit of distance is the nautical mile 
(n. mi.), which is equal to 6,076 ft, or 1,852 m. The radar range is also some- 
times given in yards, especially for artillery or short-range missile fire control. In 
some instances, when measurement accuracy is secondary to convenience, the radar 
mile is used as a unit of range. A radar mile is denned as 2,000 yd. The difference 
between it and the nautical mile is less than 1 per cent. 

Once the transmitted pulse is emitted by the radar, a sufficient length of time must 
elapse to allow any echo signals to return and be detected before the next pulse may be 
transmitted. Therefore the rate at which the pulses may be transmitted is determined 
by the longest range at which targets are expected. If the pulse repetition frequency 
were too high, echo signals from some targets might arrive before the transmission of 
the next pulse, and ambiguities in measuring range might result. Echoes that arrive 
after the transmission of the next pulse are called second-time-around (or multiple- 
time-around) echoes. Such an echo would appear to be at a much shorter range than 
the actual and could be misleading if it were not known to be a second-time-around 
echo. The range beyond which targets appear as second-time-around echoes is called 
the maximum unambiguous range and is 



d c 

Kunamb = — (1.2) 



where f r = pulse repetition frequency, in cycles per second. A plot of the maximum 
unambiguous range as a function of pulse repetition frequency is shown in Fig. 1.2. 

t Range and distance to the target are used synonymously in radar parlance although, in artillery 
usage, range is the horizontal projection of the distance. For aircraft targets, slant range is sometimes 
used to represent the distance from radar to target, and ground ranee is used for the projection of the 
slant range on the ground. J 



Sec. 1.2] The Nature of Radar 3 

Although most radars transmit a pulse-modulated waveform, there are a number of 
other suitable modulations that might be used to fulfill the functions of target detection 
and location. An example of a very important type of radar which does not use a 
pulsed carrier is the FM altimeter. Although the FM altimeter predates the application 
of radar and is not universally considered a radar, it nevertheless operates on the radar 
principle with the ground as the target. Even simple unmodulated CW transmissions 
have found application in radar. The most familiar is probably the radar speedometer, 
in widespread use by many highway police departments to enforce automobile speed 
limits. A radar employing an unmodulated CW transmission utilizes the doppler 



10,000 



TTTR 




10 



100 1,000 

Pulse repetition frequency, cps 



10,000 



Fig. 1.2. Plot of maximum unambiguous range as a function of the pulse repetition frequency, based 
onEq. (1.2). 

effect to detect the presence of moving targets. The doppler effect causes the signal 
reflected by a moving target to be shifted in frequency by an amount 

/* = y d- 3 ) 

where / d = doppler frequency, cps 

v r = relative velocity between radar and target, m/sec 
X = wavelength of carrier frequency, m 

1.2. The Radar Equation 

If the power of the radar transmitter of Fig. 1.1 is denoted by P t , and if an omni- 
directional antenna is used, that is, one which radiates uniformly in all directions, the 
power density (power per unit area) at a distance R from the radar is equal to the trans- 
mitter power divided by the surface area AttR 2 of an imaginary sphere of radius R, or 



Power density from omnidirectional antenna = 



Pt 

477R 2 



(1.4) 



Radars usually employ directive antennas, instead of omnidirectional antennas, to 
channel most of the radiated power P t into some particular direction. The gain G t of 



4 Introduction to Radar Systems [Sec. 1.2 

an antenna is a measure of the increased power radiated in the direction of the target 
as compared with the power that would have been radiated from an isotropic antenna. 
It may be denned [Eq. (7.6)] as the ratio of the maximum radiation intensity from the 
subject antenna to the radiation intensity from a lossless isotropic antenna with the 
same power input. The power density at the target from an antenna with a trans- 
mitting gain G t is 

P c 
Power density from directive antenna = — *— - (\ 5) 

The target intercepts a portion of the radiated power and reradiates it in the direction 
of the radar [Eq. (1.6)]. 

P C n 

Power reradiated in target direction = * ' (1.6) 

The parameter a is the radar cross section of the target and has the dimensions of area. . 
It is a characteristic of the target and is a measure of its size as seen by the radar. The 
power density in the echo signal at the radar receiving antenna is then 

Power density of echo signal at radar =4 — — — \ . . (11) 

7(47r/? 2 ) 2 ) ^ } 

The radar antenna captures a portion of the echo power. If the effective capture area 
of the receiving antenna is A r , the echo power P r received at the radar is 



P t G t A r a 

(477/? 2 ) 2 



p r t \j t si r <j 



This is the fundamental form of the radar equation. Note that the important antenna 
parameters are the transmitting gain and the receiving area. 
Antenna theory gives the relationship between antenna gain and effective area as 

„ ArrA t AttA t 

where the subscripts r and t refer to the receiving and transmitting antennas, respectively. 
If a common antenna is used for both transmission and reception (as is usually the case), 
the reciprocity theorem of antenna theory states that G t = G r = G and A t = A r = A '. 
Using these relationships, Eq. (1.8) becomes r " 



PtK* 

4ttA 



or P r = 7Z^ (1-106) 



P t G 2 tfo 

(4tt) 3 /? 4 



The maximum radar range i? max is the distance beyond which the target can no 
longer be detected. It occurs when the received echo signal P r just equals the minimum 
detectable signal S min . Therefore 



R, 



or R„ 



(_PjAbJ 

\4TrA 2 S mi J 

~ P t G 2 X 2 a ' 
.(AirfSram- 



(1.11a) 

min 7 



(1.11ft) 



Sec. 1.3] The Nature of Radar 5 

Equations (1.11a) and (1.116) are two forms of the radar equation which describe range 
performance. 

The above simplified versions of the radar equation do not adequately describe the 
performance of practical radars. Many important factors that affect range are not 
explicitly included. Because of the implicit nature of relationships between the param- 
eters that appear in the radar equation, one must be careful about making generaliza- 
tions concerning radar performance on the basis of these equations alone. For 
example, from Eq. (1.1 lb) it might be thought that the range of a radar varies as A*. 
On the other hand, Eq. (1.1 la) would indicate a /H relationship, and Eq. (1.8) shows 
range independent of wavelength. 

In practice, it is usually found that the observed maximum radar ranges are different 
from those predicted with the simple radar equation ( 1 . 1 1 a) or ( 1 . 1 1 b). Actual ranges 
are often much smaller than predicted. (There are some cases, however, where larger 
ranges might result, for instance, when anomalous propagation or subrefraction effects 
occur.) There are many reasons for the failure of the simple radar equation to correlate 
with actual performance, as discussed in Chap. 2. 

1.3. Radar Block Diagram and Operation 

The operation of a typical pulse radar using an oscillator such as the magnetron for 
the transmitter may be described with the aid of the block diagram shown in Fig. 1.3. 
Consider the box labeled "timer," in the upper right side of the figure. The timer, 



Duplexer 




JL 



ATR 



Transmitter 



Modulator 





w» 




» 








RF 
amplifier 




Mixer 




IF 
amplifier 




Det. 









A 



A 



Timer 



Video 
amplifier 



LO 




Fig. 1.3. Block diagram of a pulse radar. 



which is also called the trigger generator, or the synchronizer, generates a series of 
narrow timing, or trigger, pulses at the pulse repetition frequency. These timing pulses 
turn on the modulator which pulses the transmitter. Although the timer and the 
modulator both are switches, they are shown as separate boxes in the block diagram 
since different considerations enter into their design. The modulator must be capable 
of switching the high-power transmitter and might be a rather large device. On the 
other hand, the timer is of more modest proportions and only has to trigger the grid of a 
vacuum tube or thyratron. 

A typical radar used for the detection of conventional aircraft at ranges of 100 or 200 
miles might employ a peak power of the order of 1 to 10 Mw, a pulse width of several 
microseconds, and a pulse repetition frequency of several hundred pulses per second. 
The modulated RF pulse generated by the transmitter travels along the transmission 
line to the antenna, where it is radiated into space. A common antenna is usually used 
for both transmitting and receiving. A fast-acting switch called the transmit-receive 
(TR) switch disconnects the receiver during transmission. If the receiver were not 
disconnected and if the transmitter power were sufficiently large, the receiver might be 
damaged. After passage of the transmitted signal, the TR switch reconnects the 
receiver to the antenna. 




-4r. 



6 Introduction to Radar Systems [Sec. 1.3 

A portion of the radiated power is reflected by the target back to the radar and enters 
the receiver via the same antenna as used for transmitting. The ATR (anti-transmit- 
receive) switch, which has no effect during the transmission portion of the cycle, acts on 
reception to channel the received signal power into the receiver. In the absence of the 

ATR, a portion of the received power would be dissipated 
in, the transmitter rather than enter the receiver, where it 
belongs. The TR and the ATR are together called the 
duplexer. If separate antennas are employed for trans- 
mitting and receiving, a duplexer may not be necessary if 
the isolation between the two separated antennas can be 
made sufficiently large. 

The radar receiver is usually of the superheterodyne 
type. The RF amplifier shown as the first stage of the 
superheterodyne might be a low-noise parametric am- 
plifier, a traveling-wave tube, or a maser. Many micro- 
wave radar receivers do not have an RF amplifier and use 
the mixer as the first stage, or front end. The mixer 
and local oscillator (LO) convert the RF signal to an 
intermediate frequency (IF) since itis easier to build high- 
gain narrowband amplifiers at the lower frequencies. 
A typical IF amplifier might have a center frequency of 
30 or 60 Mc and a bandwidth of 1 or 2 Mc. A reflex 
klystron is commonly employed as the local oscillator. 
The RF pulse modulation is extracted by the detector 
and amplified by the video amplifier to a level where it 
can operate the indicator, usually a cathode-ray tube 
(CRT). Timing signals are also supplied to the indi- 
cator. Target positional information is obtained from 
the direction of the antenna and is used to properly 
display the coordinates of the target location. The two 
most commqn forms of indicators using cathode-ray 
tubes are the A-scope (Fig. 1.4a) and the plan position 
indicator, or PPI (Fig. 1.4b). The A-scope displays the 
target amplitude (y axis) vs. range (x axis), and no angle 
information is shown. The PPI maps the target in angle 
and range on a polar display. Target amplitude is used to modulate the electron- 
beam intensity (z axis) as the electron beam is made to sweep outward from the center 
with range. The beam rotates in angle in response to the antenna position. 

The block diagram of Fig. 1.3 is only one version of a radar. Many variations are 
possible. Furthermore, the diagram is by no means complete since it does not include 
many devices normally found in most radars. Additional devices' might include a 
means for automatically compensating the receiver for changes in radar frequency 
(AFC) or gain (AGC), receiver circuits for reducing interfering or unwanted signals, 
rotary joints in the transmission lines to allow movement of the antenna, circuitry for 
discriminating between moving targets and stationary objects (MTI), and means for 
allowing the antenna to automatically track a moving target. 

Monitoring devices (not shown) are usually employed to ensure that the radar is 
operating properly. A simple but important monitoring device is a directional coupler 
inserted in the transmission line to sample a fraction of the transmitted power. The 
output from the directional coupler may be used as a measure of the transmitted power 
or to test the fidelity of the transmitted waveform. 
A common form of radar antenna is a reflector with a parabolic shape fed from a 




Fig. 1 .4. (a) A-scopepresentation 
displaying amplitude vs. range 
(deflection modulation) ; (b) PPI 
presentation displaying range vs. 
angle (intensity modulation). 



Sec. 1.4] 



The Nature of Radar 



point source. The parabolic reflector focuses the energy into a narrow beam just as 
does an optical searchlight or an automobile headlamp. The beam may be scanned in 
space by mechanically pointing the antenna. 

1.4. Radar Frequencies 

Conventional radars have been operated at frequencies extending from about 25 to 
70,000 Mc, a spread of more than 1 1 octaves. These are not necessarily the limits 
since radars can be operated at frequencies outside either end of this range. The early 
radar developers were forced to design their equipments to operate at the lower fre- 
quencies, for the rather compelling reason that suitable components were not available 
at higher frequencies. The CH (Chain Home) radars employed by the British to 
provide early warning against air attack during World War II operated at a frequency 
in the vicinity of 25 Mc. This is a very low radar frequency by modern standards. 
Although higher transmitter powers are usually easier to achieve at the lower fre- 
quencies, the poor angular accuracy and poor resolution which result with antennas of 



Wovelength 
1km 100m 10m 



10cm 







-* VLF *- 


<— LF — *■ 


«— MF— *■ 


*— HF — *■ 


«— VHF— > 


— UHF— * 


— SHF— >■ 


<-- EHF^- 








Very low 
frequency 

i 


Low 
frequency 


Medium 
frequency 


High 
frequency 


Very high 
frequency 


Ultrahigh 
frequency 


Super 

high 
frequency 


Extremely 

high 
frequency 








My riomet ric 
waves 


Kilometric 
woves 


Hectometric 
waves 


Decometric 
waves 


Metric 
waves 


Deci metric 
waves 


Cenfi metric 
waves 


Millimetric 
waves 


Decimilli- 
metric waves 








Band 4 


Bond 5 


Bond 6 
Broadcast 


Bond 7 


Bond B 


Band 9 


Band 10 


Band 1 1 


Band 12 
Infr 




'/////////, Radar . frequencies ''/////////, 




band 


II 




Aud 


o frequenci 


s 






L 


*tter designo 


ions L S C X Ku Ka 
1 1 
Microwave region 






Video frequencies 












1 1 









30cps 300 cps 3kc 30kc 300 kc 3Mc 30 Mc 300 Mc 3Gc 30Gc 300 Gc 3,000 Gc 

Frequency 

Fig. 1.5. Radar frequencies and the electromagnetic spectrum. 

reasonable size are not suitable for most applications. The antenna beamwidth is 
inversely proportional to the size of the antenna aperture (measured in wavelengths), 
and the lower the frequency, the broader will be the beamwidth for an aperture of a 
given size. For example, at 70,000 Mc, a 1° beamwidth can be obtained with a para- 
bolic-reflector antenna approximately 1 ft in diameter. At 25 Mc, an antenna diameter 
of more than \ mile would be necessary to achieve the same beamwidth . Considerations 
such as this stimulated the development of components and techniques at the higher 
radio frequencies, known as the microwave region. 

The place of radar frequencies in the electromagnetic spectrum is shown in Fig. 1.5. 
Some of the various nomenclature employed to designate the various frequency regions 
is also shown. The radar region is shown extending from about 25 to 70,000 Mc. 
Very few modern radars are found below 200 or above 35,000 Mc. An exception to 
this are radars that operate at high frequency (HF), about 2 to 20 Mc, and take advantage 
of ionospheric reflections. Radar frequencies are not found over the entire frequency 
region. They tend to group into separate bands for reasons of economy, both in terms 
of dollars and frequency allocations. 

Early in the development of radar, a letter code such as S, X, L, etc., was employed to 
designate radar frequency bands. Although its original purpose was to guard military 
secrecy, the designations were carried over into peacetime use, probably out of habit and 



8 Introduction to Radar Systems [Sec. 1.5 

the need for some convenient short nomenclature. The more commonly used letter 
designations are indicated in Fig. 1.5 and in Table 1.1. Although these are a conven- 
ient form of nomenclature, they have no official status and there is not always general 
agreement as to the limits associated with each band. 

Two other methods of naming frequency bands shown in Fig. 1.5 are based on 
frequency subdivisions and metric subdivisions. Their use is not very precise, and 
they define only general areas. For instance, the designation ultrahigh frequency 
(UHF) usually refers, in practice, to frequencies from about 300 to about 1,000 Mc. 
In radar parlance, L or 5 band would be used to designate the UHF frequencies 
above 1,000 Mc. 

Table 1.1 
Radar frequency band Frequency 

UHF 300-1,000 Mc 

L 1,000-2,000 Mc 

S 2,000-4,000 Mc 

C 4,000-8,000 Mc 

X 8,000-12,500 Mc 

K„ 12.5-18 Gc 

K 18-26.5 Gc 

K„ 26.5-40 Gc 

Millimeter >40 Gc 

The "band" method for designating frequency as adopted by the CCIR (Comite 
Consultatif International Radio) in 1953 is also shown in Fig. 1.5. The frequency 
"band N" extends from 3 x 10* _1 to3 x lO^cps. The number of the exponent of 10 
which expresses the upper frequency limit designates the band in question. For 
example, the UHF band extending from 3 x 10 8 to 3 x 10 9 is band 9. 

The microwave region is that frequency region where distributed-constant, rather 
than lumped-constant, circuits are employed. Examples of distributed-constant 
devices are waveguides, cavity resonators, and highly directive antennas. The charac- 
teristic of the microwave region is that the size of the components is comparable with 
the wavelength. The transition between the microwave region and the lumped- 
constant region is not sharp. The lower limit of microwaves is shown as 300 Mc since 
waveguide components and power klystron amplifiers are commercially available at 
this frequency. The upper end of the microwave region is difficult to specify, but 
beyond the millimeter region, microwave techniques are more profitably replaced by 
optical techniques. 

Also shown in Fig. 1 .5 are the audio frequencies, which may be defined as the range of 
frequencies audible to the normal human ear. The video frequencies are also indicated. 
These are taken to be the range of frequencies that may be displayed on a cathode-ray 
tube. The video-frequency range is quite arbitrary. It extends from zero frequency 
to the order of several megacycles in most radar and television applications, although it 
can be considered to extend even higher since frequencies of several thousand mega- 
cycles or more may be displayed on cathode-ray tubes. 

1.5. History of Radar Development! 

Although the development of radar as a full-fledged technology did not occur until 
World War II, the basic principle of radar detection is almost as old as the subject of 
electromagnetism itself. Heinrich Hertz, in 1886, experimentally tested the theories of 
Maxwell and demonstrated the similarity between radio and light waves. Hertz 
showed that radio waves could be reflected by metallic and dielectric bodies. It is 

t Much of the material in this section concerning the early development of United States radar is 
based on an unpublished report by Guerlac. 1 



Sec. 1.5] The Nature of Radar 9 

interesting to note that although Hertz's experiments were performed with relatively 
short wavelength radiation (66 cm), later work in radio engineering was almost entirely 
at longer wavelengths. The shorter wavelengths were not actively used to any great 
extent until the late thirties. 

In 1903 a German engineer by the name of Hiilsmeyer experimented with the detec- 
tion of radio waves reflected from ships. He obtained a patent in 1904 in several 
countries for an obstacle detector and ship navigational device. 2 His methods were 
demonstrated before the German Navy, but generated little interest. The state of 
technology at that time was not sufficiently adequate to obtain ranges of more than 
about a mile, and his detection technique was dismissed on the grounds that it was little 
better than a visual observer. 

Marconi recognized the potentialities of short waves for radio detection and strongly 
urged their use in 1 922 for this application. In a speech delivered before the Institute of 
Radio Engineers, he said : 3 

As was first shown by Hertz, electric waves can be completely reflected by conducting 
bodies. In some of my tests I have noticed the effects of reflection and detection of these 
waves by metallic objects miles away. 

It seems to me that it should be possible to design apparatus by means of which a ship 
could radiate or project a divergent beam of these rays in any desired direction, which rays, 
if coming across a metallic object, such as another steamer or ship, would be reflected back 
to a receiver screened from the local transmitter on the sending ship, and thereby, immediately 
reveal the presence and bearing of the other ship in fog or thick weather. 

Although Marconi predicted and successfully demonstrated radio communication 
between continents, he was apparently not successful in gaining support for some of his 
other ideas involving very short waves. One was the radar detection mentioned 
above; the other was the suggestion that very short waves are capable of propagation 
well beyond the optical line of sight — a phenomenon now known as tropospheric 
scatter. He also suggested that radio waves be used for the transfer of power from one 
point to the other without the use of wire or other transmission lines. 

Apparently Marconi's suggestion stimulated A. H. Taylor and L. C. Young of the 
Naval Research Laboratory to confirm experimentally the speculations concerning 
radio detection. In the autumn of 1922 they detected a wooden ship using a CW 
wave-interference radar with separated receiver and transmitter. The wavelength was 
5 m. A proposal was submitted for further work but was not accepted. 

The first application of the pulse technique to the measurement of distance was in the 
basic scientific investigation by Breit and Tuve in 1925 for measuring the height of the 
ionosphere. 4 However, more than a decade was to elapse before the detection of 
aircraft by pulse radar was demonstrated. 

The first experimental radar systems operated with CW and depended for detection 
upon the interference produced between the direct signal received from the transmitter 
and the doppler-frequency-shifted signal reflected by a moving target. This effect is 
the same as the rhythmic flickering, or flutter, observed in an ordinary television 
receiver, especially on weak stations when an aircraft passes overhead. This type of 
radar originally was called CW wave-interference radar. Today, such a radar is called a 
bistatic CW radar (Sec. 13.6). The first experimental detections of aircraft used this 
radar principle rather than a monostatic (single-site) pulse radar because CW equipment 
was readily available. Successful pulse radar had to await the development of suitable 
components, especially high-peak-power tubes, and a better understanding of pulse 
receivers. 

The first detection of aircraft using the wave-interference effect was made in June, 
1930, by L. A. Hyland of the Naval Research Laboratory. 1 It was made accidentally 



10 Introduction to Radar Systems [Sec. 1.5 

while he was working with a direction-finding apparatus located in an aircraft on the 
ground. The transmitter at a frequency of 33 Mc was located 2 miles away, and the 
beam crossed an air lane from a nearby airfield. When aircraft passed through the 
beam, Hyland noted an increase in the received signal. This stimulated a more delib- 
erate investigation by the NRL personnel, but the work continued at a slow pace, 
lacking official encouragement and funds from the government, although it was fully 
supported by the NRL administration. By 1932 the equipment was demonstrated to 
detect aircraft at distances as great as 50 miles from the transmitter. The NRL work 
on aircraft detection with CW wave interference was kept classified until 1933, when 
several Bell Telephone Laboratories engineers reported the detection of aircraft during 
the course of other experiments. 5 The NRL work was disclosed in a patent filed and 
granted to Taylor, Young, and Hyland 6 on a "System for Detecting Objects by Radio." 
The type of radar described in this patent was a CW wave-interference radar. Early in 
1 934, a 60-Mc CW wave-interference radar was demonstrated by NRL. 

The early CW wave-interference radars were useful only for detecting the presence of 
the target. The problem of extracting target-position information from such radars 
was a difficult one and could not be readily solved with the techniques existing at that 
time. A proposal was made by NRL in 1933 to employ a chain of transmitting and 
receiving stations along a line to be guarded, for the purpose of obtaining some knowl- 
edge of distance and velocity. This was never carried out, however. The limited 
ability of CW wave-interference radar to be anything more than a trip wire undoubtedly 
tempered what little official enthusiasm existed for radar. 

It was recognized that the limitations to obtaining adequate position information 
could be overcome with pulse transmission. Strange as it may now seem, in the early 
days pulse radar encountered much skepticism. Nevertheless, an effort was started at 
N RL in the spring of 1 934 to develop a pulse radar. The work received low priority and 
was carried out principally by R. M. Page, but he was not allowed to devote his full time 
to the effort. 

The first attempt with pulse radar at NRL was at a frequency of 60 Mc. According 
to Guerlac, 1 the first tests of the 60-Mc pulse radar were carried out in late December, 
1934, and early January, 1935. These tests were "hopelessly unsuccessful and a 
grievous disappointment." No pulse echoes were observed on the cathode-ray tube. 
The chief reason for this failure was attributed to the receiver's being designed for CW 
communications rather than for pulse reception. The shortcomings were corrected, 
and the first radar echoes obtained at NRL using pulses occurred on Apr. 28, 1936, with 
a radar operating at a frequency of 28.3 Mc and a pulse width of 5 ^asec. The range 
was only 2\ miles. By early June the range was 25 miles. 

It was realized by the NRL experimenters that higher radar frequencies were desired, 
especially for shipboard application, where large antennas could not be tolerated. 
However, the necessary components did not exist. The success of the experiments at 
28 Mc encouraged the NRL experimenters to develop a 200-Mc equipment. The first 
echoes at 200 Mc were received July 22, 1936, less than three months after the start of 
the project. This radar was also the first to employ a duplexing system with a common 
antenna for both transmitting and receiving. The range was only 10 to 12 miles. In 
the spring of 1937 it was installed and tested on the destroyer Leary. The range of the 
200-Mc radar was limited by the transmitter. The development of higher-powered 
tubes by the Eitel-McCullough Corporation allowed an improved design of the 200-Mc 
radar known as X AF. This occurred in January, 1 938. Although the power delivered 
to the antenna was only 6 kw, a range of 50 miles — the limit of the sweep — was obtained 
by February. The XAF was tested aboard the battleship A'en- York, in maneuvers 
held during January and February of 1939, and met with considerable success. Ranges 
of 20 to 24 kiloyards were obtained on battleships and cruisers. By October, 1939, 



Sec. 1.5] The Nature of Radar 11 

orders were placed for a manufactured version called the CXAM. Nineteen of these 
radars were installed on major ships of the fleet by 1941. 

The United States Army Signal Corps also maintained an interest in radar during the 
early 1930s. 7 The beginning of serious Signal Corps work in pulse radar apparently 
resulted from a visit to NRL in January, 1936. By December of that year the Army 
tested its first pulse radar, obtaining a range of 7 miles. The first operational radar 
used for antiaircraft fire control was the SCR-268, available in 1 938. The basic patent 8 
describing the prototype of the SCR-268 was awarded to Colonel William R. Blair, a 
former director of the Signal Corps Laboratories. The claims contained in this patent 
apparently cover most of the basic ideas inherent in pulse-echo radio ranging and 
detection. Although Colonel Blair's patent may legally make him the originator of 
pulse radar, the spontaneous and independent development of pulse radar by several 
investigators in this country and abroad seems to make it difficult to assign sole credit 
to any one person for its origin. 

The SCR-268 was used in conjunction with searchlights for radar fire control. This 
was necessary because of its poor angular accuracy. However, its range accuracy was 
superior to that obtained with optical methods. The SCR-268 remained the standard 
fire-control equipment until January, 1944, when it was replaced by the SCR-584 
microwave radar. The SCR-584 could control an antiaircraft battery without the 
necessity for searchlights or optical angle tracking. 

In 1939 the Army developed the SCR-270, a long-range radar for early warning. 
The attack on Pearl Harbor in December, 1941 , was detected by an SCR-270, one of six 
in Hawaii at the time. 1 (There were also 16 SCR-268s assigned to units in Honolulu.) 
But unfortunately, the true significance of the blips on the scope was not realized until 
after the bombs had fallen. A modified SCR-270 was also the first radar to detect 
echoes from the moon in 1946. 

The early developments of pulse radar were primarily concerned with military 
applications. Although it was not recognized as being a radar at the time, the fre- 
quency-modulated aircraft radio altimeter was probably the first commercial applica- 
tion of the radar principle. The first equipments were operated in aircraft as early as 
1936 and utilized the same principle of operation as the FM-CW radar described in 
Sec. 3.3. In the case of the radio altimeter, the target is the ground. 

In Britain the development of radar began later than in the United States. 9 " 12 But 
because they felt the nearness of war more acutely and were in a more vulnerable 
position with respect to air attack, the British expended a large amount of effort on 
radar development. By the time the United States entered the war, the British were 
well experienced in the military applications of radar. British interest in radar began 
in early 1935, when Sir Robert Watson-Watt was asked about the possibility of produc- 
ing a death ray using radio waves. Watson- Watt concluded that this type of death ray 
required fantastically large amounts of power and could be regarded as not being 
practical at that time. Instead, he recommended that it would be more promising to 
investigate means for radio detection as opposed to radio destruction. (The only 
available means for locating aircraft prior to World War II were sound locators whose 
maximum detection range under favorable conditions was about 20 miles.) Watson- 
Watt was allowed to explore the possibilities of radio detection, and in February, 1935, 
he issued two memoranda outlining the conditions necessary for an effective radar 
system. In that same month the detection of an aircraft was carried out, using 6-Mc 
communication equipment, by observing the beats between the echo signal and the 
directly received signal (wave interference). The technique was similar to the first 
United States radar-detection experiments. The transmitter and receiver were 
separated by about 5.5 miles. When the aircraft receded from the receiver, it was 
possible to detect the beats to about an 8-mile range. 



12 Introduction to Radar Systems [Sec. 1.5 

By June, 1935, the British had demonstrated the pulse technique to measure range of 
an aircraft target. This was almost a year sooner than the successful NRL experiments 
with pulse radar.f By September, ranges greater than 40 miles were obtained on 
bomber aircraft. The frequency was 12 Mc. Also, in that month, the first radar 
measurement of the height of aircraft above ground was made by measuring the eleva- 
tion angle of arrival of the reflected signal. In March, 1936, the range of detection had 
increased to 90 miles and the frequency was raised to 25 Mc. 

A series of CH (Chain Home) radar stations at a frequency of 25 Mc were successfully 
demonstrated in April, 1937. Most of the stations were operating by September, 1938, 
and plotted the track of the aircraft which flew Neville Chamberlain, the British Prime 
Minister at that time, to Munich to confer with Hitler and Mussolini. In the same 
month, the CH radar stations began 24-hour duty, which continued until the end of the 
war. 

The British realized quite early that ground-based search radars such as CH were not 
sufficiently accurate to guide fighter aircraft to a complete interception at night or in bad 
weather. Consequently, they developed, by 1939, an aircraft-interception radar (AI), 
mounted on an aircraft, for the detection and interception of hostile aircraft. The Al 
radar operated at a frequency of 200 Mc. During the development of the AI radar it 
was noted that radar could be used for the detection of ships from the air and also that 
the character of echoes from the ground was dependent on the nature of the terrain. 
The former phenomenon was quickly exploited for the detection and location of surface 
ships and submarines. The latter effect was not exploited initially, but is now used for 
airborne mapping radars. 

Until the middle of 1940 the development of radar in Britain and the United States 
was carried out independently of one another. In September of that year a British 
technical mission visited the United States to exchange information concerning the 
radar developments in the two countries. The British realized the advantages to be 
gained from the better angular resolution possible at the microwave frequencies, 
especially for airborne and naval applications. They suggested that the United States 
undertake the development of a microwave AI radar and a microwave antiaircraft 
fire-control radar. The British technical mission demonstrated the cavity-magnetron 
power tube developed by Randell and Boot and furnished design information so that it 
could be duplicated by United States manufacturers. The Randell and Boot magnetron 
operated at a wavelength of 10 cm and produced a power output of about 1 kw, an 
improvement by a factor of 100 over anything previously achieved at centimeter 
wavelengths. The development of the magnetron was one of the most important 
contributions to the realization of microwave radar. 

The success of microwave radar was by no means certain at the end of 1940. There- 
fore the United States Service Laboratories chose to concentrate on the development of 
radars at the lower frequencies, primarily the very high frequency (VHF) band, where 
techniques and components were more readily available. The exploration of the 
microwave region for radar application became the responsibility of the Radiation 
Laboratory, organized in November, 1940, under the administration of the Massa- 
chusetts Institute of Technology. 

In addition to the developments carried out in the United States and Great Britain, 
radar was developed independently in France and Germany during the middle and 
late thirties. Other countries such as Japan, 14 Italy, and Russia apparently did not 
enter the field of radar until they became aligned with either Germany or the Allied 
powers. 

t Schooley 13 points out that a 60- Mc radar system was operated against aircraft in December, 1934, 
at the Naval Research Laboratory, but as indicated previously in this section, Guerlac 1 states that this 
attempt was not successful. 



Sec. 1.5] The Nature of Radar 13 

At the close of World War II most of the scientists and engineers engaged in radar 
development returned to their normal peacetime pursuits, and the pace of radar 
development slowed considerably. The radars in operational use during the decade 
following the war were, for the most part, based on designs initiated during the war. 
The AN/CPS-6B, the AN/FPS-3, and the AN/FPS-6 height finder were the primary 
radars used for long-range surveillance of aircraft in this country during that period of 
time. However, by the early fifties, some new developments became available which 
increased the capability of radar. One of the more important of these was the intro- 
duction of the high-power klystron amplifier. The high-power klystron amplifier was 
first developed not for radar application but for the linear accelerator at Stanford 
University. This is but one of many examples that illustrate how basic research can 
unpredictably contribute to the advancement of practical technology. The advantage 
of the klystron amplifier over the magnetron — the only other high-power tube used for 
microwave radar application up to that time — is that klystrons are capable of greater 
power output than magnetrons and their stability is far better, thus permitting better 
moving-target-indication (MTI) radars. 

Another component in which considerable advance has been made is the receiver. 
Advances in crystal-mixer technology and in low-noise traveling-wave tubes improved 
the sensitivity of microwave receivers by an order of magnitude. The parametric 
amplifier and the solid-state maser further improved receivers to the point where 
external noise and losses in the transmission lines are more important in determining 
receiver sensitivity than the device itself. 

During the thirties, radar development was restricted to frequencies at UHF or 
lower. During the forties, most of the significant developments were carried out in the 
microwave region. Inthe 1950s, however, there was a reversal ofthe upward frequency 
trend, and a large amount of radar development was again carried out in the UHF 
region, especially for long-range search radars. 

Another advance during the fifties was the closer integration of the radar system to 
the weapon. This was made possible primarily by the development of electronic 
computer techniques during this period. The AI radar was developed to the point 
where most ofthe functions of aiming and firing of weapons normally carried out by the 
pilot were taken over by the radar and computer. The integration of radar and 
weapon was even closer in the guided missile. In the area of air defense most of the 
functions of recognizing and plotting aircraft tracks, normally the function of an 
operator, were carried out automatically by electronic digital computers such as those 
in the SAGE (Semiautomatic Ground Environment) system. 

The post- World War II radars were more accurate and of greater range capability 
than their wartime counterparts. The accuracy of tracking radars in the fifties was an 
order of magnitude better than those ofthe previous decade. The further development 
of monopulse tracking radar also came about in this period. The need for accurate 
tracking arose mainly from the requirements of guided missiles. 

In the late 1950s, with the advent of Sputniks and intercontinental ballistic missiles, 
the range required of radars was greatly increased over that required for aircraft 
detection. This resulted in the development of radars with very high power trans- 
mitters and large antennas. 

The development of radar was sparked primarily by military needs. However, 
radar has found many civilian applications, especially in air and marine navigation. 

Radar technology is still in the process of growing. Although it may leave much to 
be desired in many applications, radar is still the only means of detecting and locating 
reflecting objects at long ranges and will continue to be used until a better substitute is 
found. 

Before this section on the history of radar development is closed, mention should be 



14 Introduction to Radar Systems [Sec. 1.6 

made of "radar" found in nature. The porpoise and the bat are both known to use 
ultrasonic echo-locating principles similar to electromagnetic radar echo location or 
ultrasonic sonar. 15 ^ 17 

The ordinary bat contains a built-in ultrasonic "radar" enabling him to fly through 
dark caves with impunity and find and catch insects on the wing for food. 17 The bat 
emits a series of ultrasonic pulses about 2 msec in width at a repetition frequency of the 
order of 10 to 20 cps under ordinary circumstances. The repetition frequency does 
vary, however, depending upon the state of activity. A bat at rest might emit pulses at 
a rate of 5 to 10 cps. In flight, for periods of time of the order of several seconds, the 
prf might be as high as 50 to 60 cps, or even higher. The shape of the transmitted 
pulse is not exactly rectangular, but rises to a maximum and then decays. Even more 
remarkable is the fact that the bat's transmission is not a simple pulse but is more like a 
frequency-modulated pulse or an FM pulse-compression waveform, as discussed in 
Sec. 10.9. The frequency-modulated transmissions emitted by one species of bat start 
at a frequency of 78 kc and decay to 39 kc, on the average. The average frequency at 
the peak amplitude of the pulse is 48 kc. Note that the length of a 2-msec ultrasonic 
pulse is 70 cm, suggesting that the bat must make use of the frequency change to indicate 
the target distance, just as do the FM radars described in Chap. 3. Bats have been 
observed to detect obstacles as close as 5 cm. The ears of the bat act the same as an 
antenna to give the bat's radar directional properties. It is found experimentally that 
the intensity of the emissions is much reduced if the bat's head is pointed 45° or more 
from the normal (assuming that the ultrasonic receiver is observing the bat head on). 
Another interesting observation is that hundreds or even thousands of bats issue from 
caves in flight without apparent difficulty from mutual interference. 

1.6. Applications of Radar 

Radar has been employed on the ground, in the air, and on the sea and undoubtedly 
will be used in space. Ground-based radar has been applied chiefly to the detec- 
tion and location of aircraft or space targets. Shipboard radar may observe other 
ships or aircraft, or it may be used as a navigation aid to locate shore lines or buoys. 
Airborne radar may be used to detect other aircraft, ships, or land vehicles, or it may 
be used for storm avoidance and navigation. The nature of the vehicle that carries 
the radar and the environment in which it operates have a significant influence on its 
design. 

Civilian Applications. The chief use of radar outside of the military has been for 
navigation, both marine and air. Air-trafnc-control radar monitors air traffic in the 
vicinity of airports and en route between air terminals. In foul weather, radar is used 
with GCA (ground control of approach) systems to guide aircraft to a safe landing. 
Commercial aircraft carry radar altimeters to determine their height above the ground 
and weather-avoidance radar to navigate around dangerous storms. 

On the sea, radar is used by ships, large and small, for navigation, especially in bad 
weather or with poor visibility. Radar has also been used as an aid in surveying over 
very large distances. One of the more important applications of radar is in the detection 
and tracking of weather disturbances, especially tornadoes and hurricanes. 

Perhaps the application with which the reader has had most contact is the speed- 
measuring radar used by many of the highway police. 

Military Applications. A large number of the civilian applications of radar men- 
tioned above also apply to the military, especially radar navigation. In addition, radar 
is used by the military for surveillance and for the control of weapons. Surveillance 
radars detect and locate hostile targets for the purpose of taking proper military action. 
Examples of such radars are those in the DEW (Distant Early Warning) line for the 
detection of aircraft; the BMEWS (Ballistic Missile Early Warning System) radars for 




Fig. 1.6. AN/FPS-24 long-range search radar. (Courtesy General Electric Co., Heavy Military 
Electronics Department.) 




mm 



Fig. 1.7. Portable surveying radar MRA-2 Tellurometer system. (Courtesy Tellurometer, Inc.) 

15 




Fig. 1.8. AN/SPG-49 Talos missile-tracking radars on board the U.S.S. Galveston. (Courtesy 
Sperry Gyroscope Co.) 




Fig. 1.9. AN/MPQ-10 mortar-detection radar. (Courtesy Sperry Gyroscope Co.) 

16 



Sec. 1.6] 



The Nature of Radar 



17 



detecting and tracking intercontinental ballistic missiles ; the long-range search radars 
of the SAGE system; shipboard surveillance radars; and the AEW (Airborne Early 
Warning) radars. 

Examples of radars for the control of weapons include the acquisition radars and 
tracking radars of air defense systems such as those of Nike, homing radars on guided 
missiles, AI (airborne-interception) radar used to guide a fighter aircraft to its target, 
and bombing radars. 

Scientific Applications. The use of radar 
as a measurement tool by research scientists 
has vastly increased our knowledge of mete- 
orology, aurora, meteors, and other objects 
of the solar system. Radar can guide space 
vehicles and satellites and may be used for 
the exploration of interplanetary space. 
In addition, the techniques and components 
developed for radar have been put to good 
use in such basic research as microwave 
spectroscopy, radio astronomy, and radar 
astronomy. 

Examples. Some of the many varied 
shapes radars may take are illustrated in 
Figs. 1.6 to 1.12. The AN/FPS-24 (Fig. 
1.6) is a large frequency-diversity radar 
(Sec. 12.10) for the surveillance of aircraft. 
Its antenna is 120 ft wide and 36 ft high. 
The reflector, pedestal, and feed horn weigh 
more than 135 tons. A beacon interro- 
gating antenna (Sec. 13.7) is mounted on 
top. 

This large radar is contrasted with the 
30-lbMRA-2 Tellurometer surveying radar 
(Fig. 1.7), a small portable equipment 
capable of precisely measuring the distance 
between two points (Sec. 3.5). 

Figure 1.8 shows two AN/SPG-49 missile-tracking radars mounted on board ship. 
Their function is to automatically acquire and track targets for the Talos surface-to-air 
missile systems. The two smaller dish-shaped radars are the AN/SPW-2, used to guide 
the missile to the target. A mortar-detection radar, the AN/MPQ-10, is shown in 
Fig. 1.9. 

Figure 1.10 illustrates the 22-in.-diameter antenna for the RDR-1D airborne weather 
radar system (Sec. 13.5) designed to be mounted in the nose of an aircraft. A spoiler 
grid is shown in the upper half of the antenna to provide a cosecant-squared beam (Sec. 
7.9) for improved ground mapping. 

The Frescan radar shown in Fig. 1 . 1 1 is a three-dimensional (3-D) pencil-beam radar. 
Elevation coverage is obtained with electronic frequency scanning (Sec. 7.7), while 
azimuth scanning is obtained by mechanical rotation of the antenna. The antenna 
beam is stabilized electronically to compensate for the pitch and roll of a ship at 
sea. 

An example of an electronically scanned array radar is ESAR (Fig. 1.12 and Sec. 
7.7). The sloping face of the building measures 50 by 50 ft. The antenna is fixed, and 
the beam position is controlled electronically. 




Fig. 1.10. RDR-1D airborne-weather-radar- 
system antenna. (Courtesy Bendix Radio.) 




Fig. 1.11. Frescan 3-D radar mounted on the masthead of the missile cruiser U.S.S. Galveston. 
(Courtesy Hughes Aircraft Co.) 




Fig. 1.12. ESAR, electronically steered array radar. (Radar to the left rear is the AN/FPS-18 gap- 
filler radar.) {Courtesy Bendix Radio.) 



18 



The Nature of Radar 19 



REFERENCES 



1. Guerlac, H. E.: "OSRD Long History," vol. V, Division 14, "Radar," available from Office of 
Technical Services, U.S. Department of Commerce. 

2. British Patent 13,170, issued to Christian Hulsmeyer, Sept. 22, 1904, entitled "Hertzian-wave 
Projecting and Receiving Apparatus Adapted to Indicate or Give Warning of the Presence of a 
Metallic Body, Such as a Ship or a Train, in the Line of Projection of Such Waves." 

3. Marconi, S. G. : Radio Telegraphy, Proc. IRE, vol. 10, no. 4, p. 237, 1922. 

4. Breit, G., and M. A. Tuve: A Test of the Existence of the Conducting Layer, Phys. Rev., vol. 28, 
pp. 554-575, September, 1926. 

5. Englund, C. R., A. B. Crawford, and W. W. Mumford: Some results of a Study of Ultra-short- 
wave Transmission Phenomena, Proc. IRE, vol. 21, pp. 475-492, March, 1933. 

6. U.S. Patent 1,981,884, "System for Detecting Objects by Radio," issued to A. H. Taylor, L. C. 
Young, and L. A. Hyland, Nov. 27, 1934. 

7. Vieweger, A. L.: Radar in the Signal Corps, IRE Trans., vol. MIL-4, pp. 555-561, October, 1960. 

8. U.S. Patent 2,803,819, "Object Locating System," issued to W. R. Blair, Aug. 20, 1957. 

9. Origins of Radar: Background to the Awards of the Royal Commission, Wireless World, vol. 58, 
pp. 95-99, March, 1952. 

10. Wilkins, A. F.: The Story of Radar, Research (London), vol. 6, pp. 434-440, November, 1953. 

11. Rowe, A. P.: "One Story of Radar," Cambridge University Press, New York, 1948. A very 
readable description of the history of radar development at TRE (Telecommunications Research 
Establishment, England) and how TRE went about its business from 1935 to the end of World 
War II. 

12. Watson- Watt, Sir Robert : "Three Steps to Victory," Odhams Press, Ltd., London, 1957 ; "The Pulse 
of Radar," The Dial Press, Inc., New York, 1959. 

13. Schooley, A. W.: Pulse Radar History, Proc. IRE, vol. 37, p. 405, April, 1949. 

14. Wilkinson, R. I.: Short Survey of Japanese Radar, Elec. Eng., vol. 65, pp. 370-377, August- 
September, 1946, and pp. 455^163, October, 1946. 

15. Griffin, D.. R.: "Listening in the Dark," Yale University Press, New Haven, Conn., 1958. 

16. Griffin, D. R.: "Echoes of Bats and Men," Doubleday & Company, New York, 1959. 

17. Griffin, D. R.: Measurements of the Ultrasonic Cries of Bats, J. Acoust. Soc. Am., vol. 22, 
pp. 247-255, 1950. 



2 



THE RADAR EQUATION 



2.1. Prediction of Range Performance 

The simple form of the radar equation derived in Sec. 1.2 expressed the maximum 
radar range R max in terms of radar and target parameters : 

P t GA e a 



Rr, 



(2.1) 



_(477) 2 S min J 

where P t — transmitted power, watts 
G = antenna gain 
A e = antenna effective aperture, m 2 
a .= radar cross section, m 2 
Smin = minimum detectable signal, watts 
All the parameters are to some extent under the control of the radar designer, except for 
the target cross section a. The radar equation states that if long ranges are desired, the 
transmitted power must be large, the radiated energy must be concentrated into a 
narrow beam (high transmitting antenna gain), the received echo energy must be 
collected with a large antenna aperture (also synonymous with high gain), and the 
receiver must be sensitive to weak signals. 

In practice, however, the simple radar equation does not predict the range perform- 
ance of actual radar equipments to a satisfactory degree of accuracy. The predicted 
values of radar range are usually optimistic. In some cases the actual range might be 
only half that predicted. 1 Part of this discrepancy is due to the failure of Eq. (2. 1) to 
explicitly include the various losses that can occur throughout the system or the loss in 
performance usually experienced when electronic equipment is operated in the field 
rather than under laboratory-type conditions. Another important factor that must be 
considered in the radar equation is the statistical or unpredictable nature of several of 
the parameters. The minimum detectable signal S min and the target cross section a are 
both statistical in nature and must be expressed in statistical terms. Other statistical 
factors which do not appear explicitly in Eq. (2. 1) but which have an effect on the radar 
performance are the meteorological conditions along the propagation path and the 
performance of the radar operator, if one is employed. The statistical nature of these 
several parameters does not allow the maximum radar range to be described by a single 
number. Its specification must include a statement of the probability that the radar 
will detect a certain type of target at a particular range. 

In this chapter, the simple radar equation will be extended to include most of the 
important factors that influence radar range performance. If all those factors affecting 
radar range were known, it would be possible, in principle, to make an accurate pre- 
diction of radar performance. But, as is true for most endeavors, the quality of the 
prediction is a function of the amount of effort employed in determining the quantitative 
effects of the various parameters. Unfortunately, the effort required to specify 
completely the effects of all radar parameters to the degree of accuracy required for 
range prediction is usually not economically justified. A compromise is always 
necessary between what one would like to have and what one can actually get with 
reasonable effort. This will be better appreciated as we proceed through the chapter 
and note the various factors that must be taken into account. 

20 



Sec. 2.2] 



The Radar Equation 21 



A complete and detailed discussion of all those factors that influence the prediction of 
radar range is beyond the scope of a single chapter. For this reason many subjects 
will appear to be treated only lightly. This is deliberate and is necessitated by brevity. 
More detailed information will be found in some of the subsequent chapters or in the 
references listed at the end of the chapter. 

2.2. Minimum Detectable Signal 

The ability of a radar receiver to detect a weak echo signal is limited by the noise 
energy that occupies the same portion of the frequency spectrum as does the signal 
energy. The weakest signal the receiver can detect is called the minimum detectable 
signal. The specification of the minimum detectable signal is sometimes difficult 
because of its statistical nature and because the criterion for deciding whether a target is 
present or not may not be too well defined. This is especially true if a human operator 
makes the detection decision. 

Detection is based on establishing a threshold level at the output of the receiver. If 
the receiver output exceeds the threshold, a signal is assumed to be present. This is 
called threshold detection. Consider the output of a typical radar receiver as a function 



Threshold level 




Time 



Fig. 2.1 . Typical envelope of the radar receiver output as a function of time. 



of time (Fig. 2. 1). This might represent one sweep of the video output displayed on an 
A-scope with the receiver gain turned all the way up to make the noise level visible. 
The envelope has a fluctuating appearance caused by the random nature of noise. If a 
large signal is present such as at A in Fig. 2.1, it is greater than the surrounding noise 
peaks and can be recognized on the basis of its amplitude. Thus, if the threshold level 
were set sufficiently high, the envelope would not generally exceed the threshold if noise 
alone were present, but would exceed it if a strong signal were present. If the signal 
were small, however, it would be more difficult to recognize its presence. The threshold 
level must be low if weak signals are to be detected, but it cannot be so low that noise 
peaks cross the threshold and give a false indication of the presence of targets. 

The voltage envelope of Fig. 2. 1 is assumed to be from a matched-filter receiver 
(Sec. 9.2). A matched filter is one designed to maximize the output peak signal to 
average noise (power) ratio. This is not the same as the concept of "impedance match" 
of circuit theory. The ideal matched-filter receiver cannot always be exactly realized 
in practice, but it is possible to approach it with practical receiver circuits. A nearly 
matched filter receiver for a radar transmitting a rectangular-shaped pulse is usually 
characterized by a bandwidth B approximately the reciprocal of the pulse width t, or 
Br ph 1 . The output of a matched-filter receiver is the cross correlation between the 
received waveform and the impulse response of the filter. Hence it does not preserve 
the shape of the input waveform. Other receiver design techniques must be employed 
if it is necessary to reproduce faithfully the shape of the input waveform. One such 
technique is the least-square smoothing and prediction theory of Wiener. 2 



24 Introduction to Radar Systems 



[Sec. 2.3 



important except to know that it exists. A discussion of the additional noise sources 
in nonideal receivers is given in Sec. 8.3. No matter whether the noise is generated by a 
thermal mechanism or by some other mechanism, the total noise at the output of the 
receiver may be considered to be equal to the thermal-noise power obtained from an 
ideal receiver multiplied by a factor called the noise figure. The noise figure F n of a 
receiver is defined by the equation 

,, N noise out of practical receiver ,. . , 

F n =-- 2 — — a (2.4a) 

kT B n G a noise out of ideal receiver at std temp T 
where N = noise output from receiver 

G a = available gain 
The temperature T is taken to be 290°K, according to the Institute of Radio Engineers 
definition. The noise N is measured over the linear portion of the receiver input- 
output characteristic, usually at the output of the IF amplifier before the nonlinear 

Table 2.1. Comparison of Noise Bandwidth and 3-db Bandwidth! 



Type of receiver 


No. of stages 


Ratio of noise bandwidth 


coupling circuit 


to 3-db bandwidth 


Single-tuned 


1 


1 57 




2 


1.22 




3 


1.16 




4 


1.14 


Double-tuned { 


5 
1 


1.12 
1.11 


Staggered triple 

Staggered quadruple . . . 
Staggered quintuple . . . 
Gaussian 


2 
1 
1 
1 
1 


1.04 
1.048 
1.019 
1.01 
1 065 







t J. L. Lawson and G. E. Uhlenbeck (eds.): "Threshold Signals," MIT Radiation Laboratory 
Series, vol. 24, p. 177, McGraw-Hill Book Company, Inc., New York, 1950. 

X Applies to a transitionally coupled double-tuned circuit or to a stagger-tuned circuit with two 
tuned circuits. 

second detector. The receiver bandwidth B n is that of the IF amplifier in most re- 
ceivers. The available gain G a is the ratio of the signal out S B to the signal in S t , and 
kT oK is the input noise A",, in an ideal receiver. Equation (2.4a) may be rewritten as 

r- _S t IN t 



S IN 



(2.4b) 



The noise figure may be interpreted, therefore, as a measure of signal-to-noise-ratio 
degradation as the signal passes through the receiver. In Chap. 8, noise figure is 
shown to depend upon the configuration of the first few input stages and the frequency 
of operation. In general, better noise figures occur at lower frequencies. 
Rearranging Eq. (2.46), the input signal may be expressed as 

<j _ kT B n F n S o 
N 

If the minimum detectable signal S min is that value of 5, corresponding to the minimum 
ratio of ouput (IF) signal-to-noise ratio (S /N ) m m necessary for detection, then 



(2.5) 



= kT B 



»'«1»j / 

\Ay m in 



(2.6) 

v </min 

This assumes that the input receiver noise is kT Q B n . For many radar applications this 
assumption is satisfactory. However, it is strictly applicable only when the receiver 



Sec. 2.4] The Radar Equation 25 

input is at the standard temperature 290°K. When the receiver is connected to an 
antenna, the temperature seen by the receiver may be lower or higher than 290°K. 
With relatively noisy receivers, the effect of an antenna temperature different from 
290°K would hardly be noticed unless the temperature were high. However, with 
low-noise receivers resulting from the use of the maser and the parametric amplifier, the 
effect of antenna temperature is important (Sec. 8.6). An alternative description of 
receiver noise, especially useful when dealing with low-noise receivers, is the effective 
noise temperature discussed in Sec. 8.5. 

Substituting Eq. (2.6) into Eq. (2. 1) results in the following form of the radar equation : 

n4 __ PfiA e o <2 j. 

maX (47rfkT B n F n (SjN ) mln 
Before continuing the discussion of the factors involved in the radar equation, it is 
necessary to digress and review briefly some topics in probability theory in order to 
describe the signal-to-noise ratio in statistical terms. 

2.4. Probability-density Functions 

The basic concepts of probability theory needed in solving noise problems may be 
found in any of several references. 4 "" 8 In this section we shall briefly review probability 
and the probability-density function and cite some examples. 

Noise is a random phenomenon. It cannot be precisely predicted any more than one 
can predict the name of a card blindly drawn from a shuffled deck. Predictions con- 
cerning the average performance of chance events are possible by observing and classify- 
ing occurrences, but one cannot predict exactly what will occur for any particular event. 
Phenomena of a random nature can be described with the aid of probability theory. 

Probability is a measure of the likelihood of occurrence of an event. Consider a 
particular experiment in which there are n different possible outcomes, all of which are 
equally likely. If the event E occurs m times out of a possible total of n, the probability 
of the event E is the ratio mjn. For example, the probability of drawing the ace of 
spades from a deck of 52 cards is 1/52, the probability ofdrawinganyaceis4/52 = 1/13, 
and the probability of drawing any spade is 13/52 = 1/4. The scale of probability 
ranges from to l.f An event which is certain is assigned the probability 1. An 
impossible event is assigned the probability 0. The intermediate probabilities are 
assigned so that the more likely an event, the greater is its probability. 

One of the more useful concepts of probability theory needed to analyze the detection 
of signals in noise is the probability-density function. Consider the variable x as 
representing a typical measured value of a random process such as a noise voltage or 
current. Imagine each x to define a point on a straight line corresponding to the 
distance from a fixed reference point. The distance of x from the reference point might 
represent the value of the noise current or the noise voltage. Divide the line into small 
equal segments of length Ax and count the number of times that x falls in each interval. 
The probability-density function p{x) is then defined as 

, . ,. (number of values in range Ax at x)/Ax ,„ „. 

p(x) = lim (2.8) 

Aa->o total number of values = N 

The probability that a particular measured value lies within the infinitesimal width dx 
centered at x is simply p{x) dx. The probability that the value of x lies within the finite 
range from x x to x 2 is found by integrating p{x) over the range of interest, or 

Probability (x x < x < x 2 ) = p(x) dx (2.9) 

t Probabilities are sometimes expressed in per cent (0 to 100) rather than to 1. 



26 Introduction to Radar Systems [S ec . 2.4 

By definition, the probability-density function is positive. Since every measurement 
must yield some value, the integral of the probability density over al 1 values of x must be 
equal to unity; that is, 

p(x)dx=l (2.10) 

The average value of a variable function, <f>(x), that is described by the probability- 
density function, p(x), is 

(<t>(x)) av = \ <f>(x)p(x)dx (2.11) 

J — qo 

This follows from the definition of an average value and the probability-density function. 
The mean, or average, value of x is 

<x)av = m x =\ xp(x) dx (2.12) 

and the mean-square value is 

<x 2 )av = m 2 = x 2 p(x) dx (2.13) 

•/ — CO 

The quantities m 1 and m 2 are sometimes called the first and second moments of the 
random variable x. If x represents an electric voltage or current, m x is the d-c com- 
ponent. It is the value read by a direct-current voltmeter or ammeter. The mean- 
square value (m 2 ) of the current when multiplied by the resistance! gives the mean power. 
The mean-square value of voltage times the conductance is also the mean power. The 
variance is defined as 

jx 2 = a 2 = ((x - mi )\ v = ( X - mi ) 2 p(x) dx = m 2 - m\ = (x 2 ) av - {x)h 

v ~ QO 

(2.14) 
The variance is the mean-square deviation of x about its mean and is sometimes called 
the second central moment. If the random variable is a noise current, the product of 
the variance and resistance gives the mean power of the a-c component. The square 
root of the variance a is called the standard deviation and is the root-mean-square (rms) 
value of the a-c component. 

We shall consider three examples of probability-density functions, the uniform 
Gaussian, and the Rayleigh. The uniform probability-density (Fig. 2.2a) is defined as 

p(x)= ik fora<x<a 



[0 for x < a and x > a + b 
where k is a constant. A rectangular, or uniform, distribution describes the phase of a 
random sine wave relative to a particular origin of time; that is, the phase of the sine 
wave may be found, with equal probability, anywhere from to 2tt, with k = 1 I2tt It 
also applies to the distribution of the round-off (quantizing) error in numerical com- 
putations. 

The constant k may be found by applying Eq. (2.10); that is, 



p(x) dx = 

" oo J a 



k dx = 1 or k = - 
b 
The average value of x is 

b 



1_ J. ~b 
t In noise theory it is customary to take the resistance as 1 ohm or the conductance as 1 mho. 



m 1 = | - x dx = a 

2 



Sec. 2.4] The Radar Equation 27 

This result could have been determined by inspection. The second-moment, or 
mean-square, value is 

[ a + b x 2 , , , , , b 2 

™2 = 

Ja 

and the variance is 



— dx = a 2 + ab , 
b 3 



m 9 — m. 



12 



a = standard deviation 



2^3 



a* b 



(a) 





Fig. 2.2. Examples of probability-density functions, (a) Uniform; (6) Gaussian; (c) Rayleigh 
(voltage); (d) Rayleigh (power), w = x 2 . 

The Gaussian, or normal, probability density (Fig. 2.2b) is one of the most important 
in noise theory, since many sources of noise, such as thermal noise or shot noise, may be 
represented by Gaussian statistics. Also, a Gaussian representation is often more 
convenient to manipulate mathematically. The Gaussian density function has a 
bell-shaped appearance and is denned by 



p(x) = 



sjlna- 



exp 



-(x - x ) 2 
2o- 2 



(2.15) 



where exp [ ] is the exponential function, and the parameters have been adjusted to 
satisfy the normalizing condition of Eq. (2. 10). It can be shown that 



ij = xp(x) dx = x m 2 = x 2 p(x) dx = x% + a 2 

J — CO J — X 



^2 = m 2 — m 1 = a 2 



(2.16) 

The probability density of the sum of a large number of independently distributed 
quantities approaches the Gaussian probability-density function no matter what the 
individual distributions may be, provided that the contribution of any one quantity is 



28 Introduction to Radar Systems [Sec. 2.4 

not comparable with the resultant of all others. This is the central limit theorem. It is 
the reason that shot noise resulting from the impact of electrons upon the anode of a 
vacuum tube can be represented by a Gaussian distribution, even though the electrons 
are emitted from the cathode with other than a Gaussian distribution. 

Another interesting property of the Gaussian distribution is that no matter how large 
a value x we may choose, there is always some finite probability of finding a greater 
value. If the noise at the input of the threshold detector were truly Gaussian, then no 
matter how high the threshold were set, there would always be a chance that it would be 
exceeded by noise and appear as a false alarm. However, the probability diminishes 
rapidly with increasing x, and for all practical purposes the probability of obtaining an 
exceedingly high value of x is negligibly small and may be regarded as being almost 
impossible. 

As an example of the Gaussian density function, consider the problem of determining 
the d-c component at the output of a linear half-wave rectifier when the input is thermal 
noise. The probability-density function of the input noise is assumed to be Gaussian 
with zero mean. The probability that the input-noise voltage will lie between x and 
x + dx is 

1 —x 2 

p(x) dx = . — exp — - dx — oo < x < oo 

V27ror 2a 2 

The output y of the half-wave rectifier for an input x is 

y = ax x > 
j=0 x<0 

The probability that the rectifier output y > will lie between y and y + dy is the same 
as the probability that x lies between x and x + dx when x > 0: 

1 —v 2 

P(y) dy = p(x) dx = ■ exp —f- dy for x > 

^iirao 2a i a i 

The probability of obtaining y = is the same as x < 0, which is exactly \. Since 
negative values of y are not permitted, the probability of y < is zero. Therefore the 
probability-density function for the output of a linear half-wave rectifier with a Gaussian 
noise input is 



1 _ v 2 

P(y) dy = — . exp — f- dy + \d(y) dy y > 



yjliraa 2a 2 a 2 
n (imj 

d(y) = y ^ 



where d(y) is the Dirac delta function (impulse function) and has the following prop- 
erties : 



+ E 

6(y) dy = 1 e > 



/•0 + e 
1 



Note that/?(j) has both a continuous and a discrete part. 
The average value, or d-c component, of the output y is 

f 00 1 f°° — v 2 1 f°° 

(y)av = yp(y) dy = -=- y exp -f- dy + - \ y d(y) dy 
«'-<>° Jliraa Jo 2a"cr 2J-oo 



2 2 — y 2 
IT- ~ aa ex P TT 



0=^ 



V2^ 



The Rayleigh probability-density function is also of special interest to the radar 
systems engineer. It describes the noise output from a narrowband filter (such as the 



Sec. 2.5] The Radar Equation 29 

IF filter in a superheterodyne receiver), the cross-section fluctuations of certain types of 

complex radar targets, and many kinds of clutter and weather echoes. The Rayleigh 

density function is 

2x / x 2 \ 
p(x) dx = — — exp I — I dx x > (2.17) 

<X 2 )av \ <X 2 >av/ 

The parameter x might represent a voltage, and (x 2 } av the mean, or average, value of the 
voltage squared. If x 2 is replaced by w, where w represents power instead of voltage 
(assuming the resistance is 1 ohm), the Rayleigh density function is 

p(w) dw = — exp I \ dw w > (2.18) 

w \ w / 

where w is the average power. A typical plot of the Rayleigh density function for x is 
shown in Fig. 2.2c and for w in Fig. 2.2d. The standard deviation of the Rayleigh 
density is equal to the mean value (x 2 ) av in Eq. (2.17) and w in Eq. (2.18). 

Another mathematical description of statistical phenomena is the probability 
distribution function P(x), defined as the probability that the value x is less than some 
specified value 



P(x)= p(x)dx or p(x) = —P(x) (2.19) 

J-oo dx 

In some cases, the distribution function may be easier to obtain from an experimental 
set of data than the density function. The density function may be found from the 
distribution function by differentiation. 

2.5. Signal-to-noise Ratio 

In this section the results of statistical noise theory will be applied to obtain the 
signal-to-noise ratio at the output of the IF amplifier necessary to achieve a specified 
probability of detection without exceeding a specified probability of false alarm. The 



IF 
omplifier 

(%) 



Second 
detector 



Video 

omplifier 

(By) 



Fig. 2.3. Envelope detector. 

output signal-to-noise ratio thus obtained may be substituted into Eq. (2.6) to find the 
minimum detectable signal, which, in turn, is used in the radar equation, as in Eq. (2.7). 

Consider an IF amplifier with bandwidth B IF followed by a second detector and a 
video amplifier with bandwidth B v (Fig. 2.3). The second detector and video amplifier 
are assumed to form an envelope detector, that is, one which rejects the carrier frequency 
but passes the modulation envelope. To extract the modulation envelope, the video 
bandwidth must be wide enough to pass the low-frequency components generated by 
the second detector, but not so wide as to pass the high-frequency components at or near 
the intermediate frequency. The video bandwidth B v must be greater than 5 IF /2 in 
order to pass all the video modulation. Most radar receivers used in conjunction with 
an operator viewing a CRT display meet this condition and may be considered envelope 
detectors. Either a square-law or a linear detector may be assumed since the effect on 
the detection probability by assuming one instead of the other is small (Sec. 9.6). 

The noise entering the IF filter (the terms filter and amplifier are used interchangeably) 
is assumed to be Gaussian, with probability-density function given by 

1 —v 2 
p(v) dv = exp dv (2.20) 

y/2iry) 2^o 



30 



Introduction to Radar Systems 



[Sec. 2.5 

where p(v) dv is the probability of finding the noise voltage v between the values of v and 
v + dv, y> is the variance, or mean-square value of the noise voltage, and the mean value 
of v is taken to be zero. If Gaussian noise were passed through a narrowband IF 
filter— one whose bandwidth is small compared with the mid-frequency— the proba- 
bility density of the envelope of the noise voltage output is shown by Rice 9 to be 



p(R) dR = - exp (- — ) dR 



(2.21) 



where R is the amplitude of the envelope of the filter output. Equation (2.2 1 ) is a form 
of the Rayleigh probability-density function. 

The probability that the envelope of the noise voltage will lie between the values of V x 
and V 2 is 

Probability (V x < R < V 2 ) = \ * ' - exp (- — ) dR (2.22) 

The probability that the noise voltage envelope will exceed the voltage threshold V T is 

f °° R I R 2 \ 

Probability (V T < R < oo) = — exp - — \ dR (2.23) 

Jv T rp \ 2y> ! 

= exp (--^1 =Pfa (2.24) 

\ 2wJ 



Whenever the voltage envelope exceeds the threshold, a target detection is considered to 
have occurred, by definition. Since the probability of a false alarm is the probability 
that noise will cross the threshold, Eq. (2.24) gives the probability of a false alarm, 
denoted P {iX . 

The average time interval between crossings of the threshold by noise alone is defined 
as the false-alarm time\ 7}„, 



T ft 



1 v 
= Um±YT k 

.Y-ao JV* = 1 



where T k is the time between crossings of the threshold V T by the noise envelope, when 
the slope of the crossing is positive. The false-alarm probability may also be defined 
as the duration of time the envelope is actually above the threshold to the total time it 




Time ■ 



Fig. 2.4. Envelope of receiver output illustrating false alarms due to noise. 

t This definition differs from that given by Marcum, 10 who defines the false-alarm time to be the 
time in which the probability is J that a false alarm will not occur. A comparison of the two 
definitions is given by Hollis. 11 



Sec. 2.5] 

could have been above the threshold, or 



Pfa = 



A' 

k = l __ Wav 

N 

XT* 



<r*>, 



*/av 



T,aB 



The Radar Equation 31 



(2.25) 



where t k and T k are defined in Fig. 2.4. The average duration of a noise pulse is 
approximately the reciprocal of the bandwidth B, which in the case of the envelope 
detector is B 1F . [It does not matter in most applications whether the bandwidth is that 
defined by the half-power points or by noise considerations, as in Eq. (2.3).] Equating 
Eqs. (2.24) and (2.25), we get 



Tfa 



1 



K 



exp- 
Bif 2y 



(2.26) 



A plot of Eq. (2.26) is shown in Fig. 2.5, with V^j2\p as the abscissa. If, for example, 
the bandwidth of the IF amplifier were 1 Mc and the average false-alarm time that could 
be tolerated were 15 min, the probability of a false alarm is 1.11 x 10~ 9 . From Eq. 
(2.24) the threshold voltage necessary to achieve this false-alarm time is 6.45 times the 
rms value of the noise voltage. 



10,000 




15 min 



Threshold-to-noise ratio V T /Z i// , d b 



Fig. 2.5. Average time between false alarms as a function of the threshold level V T and receiver 
bandwidth B; y>„ is the mean-square noise voltage. 



32 Introduction to Radar Systems [Sec. 2.5 

The false-alarm probabilities of practical radars are quite small. The reason for this 
is that the false-alarm probability is the probability that a noise pulse will cross the 
threshold during an interval of time approximately equal to the reciprocal of the band- 
width. For a 1-Mc bandwidth, there are of the order of 10 6 noise pulses per second. 
Hence the false-alarm probability of any one pulse must be small (< 10 -6 ) if false-alarm 
times greater than 1 sec are to be obtained. 

The specification of a tolerable false-alarm time usually follows from the requirements 
desired by the customer and depends on the nature of the radar application. The 
exponential relationship between the false-alarm time 7> a and the threshold level V T 
results in the false-alarm time being sensitive to variations or instabilities in the threshold 
level. For example, if the bandwidth were 1 Mc, a value of 10 log 10 ( Kf./2y ) = 12.95 
db results in an average false-alarm time of 6 min, while a value of 10 log 10 ( Kf./2y ) = 
14.72 db results in a false-alarm time of 10,000 hr. Thus a change in the threshold 
of only 1 .77 db changes the false-alarm time by five orders of magnitude. Such is the 
nature of Gaussian noise. In practice, therefore, the threshold level would probably 
be adjusted slightly above that computed by Eq. (2.26), so that instabilities which lower 
the threshold slightly will not cause a flood of false alarms. 

If the receiver were turned off (gated)for a fraction of time (as in atracking radar with 
a servo-controlled range gate or a radar which turns the receiver off during the time of 
transmission), the false-alarm probability will be reduced by the fraction of time the 
receiver is not operative. On the other hand, if the radar output consists of more than 
one independent channel, the false-alarm probability will be increased accordingly. 
However, these effects are usually not important since small changes in the probability 
of false alarm result in even smaller changes in the threshold level because of the expo- 
nential relationship of Eq. (2.26). 

The formulation of the false-alarm probability given above is only approximate, 
primarily because of the assumption that Br & 1 . Errors in this approximation are 
not serious in practice because of the exponential relationship between the threshold and 
the probability of false alarm. 

An equivalent interpretation of the false-alarm probability is as follows. On the 
average there will be one false decision out of n f possible decisions in the false-alarm 
time r fa . The average number of possible decisions between false alarms is the false- 
alarm number n t . The number of decisions n f in time 7> a is equal to the number of range 
intervals per pulse period t] = T r jr = \jf r r, times the number of pulse periods per 
second/,., times the false-alarm time 7>„, where t is the pulse width, T r the pulse repetition 
period, and/ r = 1/7; is the pulse repetition frequency. Therefore the number of 
possible decisions is n t = T {ll f r fj = T { Jr. Since t ^ IjB, where B is the bandwidth, 
the false-alarm probability is P fa = \\n s = \\T iA B as before. If n pulses are added 
together (integrated) so as to improve detection, the number of independent decisions 
in the time T u will be reduced by a factor n. The probability of false alarm will then be 
P fa = njn,. Whenever appropriate, P ia will be used in this text instead of n f . How- 
ever, the data of Marcum 10 and Swerling 34 pertaining to integration loss presented later 
in this chapter are given in terms of n f rather than P til . 

It has been shown that, in theory, the false-alarm probability due to Gaussian noise 
may be reduced to an insignificant level by the proper selection of the threshold. In 
practice, other sources of noise can enter the receiver and falsely cause an alarm to be 
excited. Such sources of noise might be local-site noise due to ignition systems, 
power-line surges, electric razors, microphonics, etc. These can be avoided only 
by good engineering design or by recognizing them as non-Gaussian noise and not 
signal. 

Thus far, a receiver with only a noise input has been discussed. Next, consider a 
sine-wave signal of amplitude A to be present along with noise at the input to the IF 



Sec. 2.5] The Radar Equation 33 

filter. The frequency of the signal is the same as the IF midband frequency / IF . The 
output of the envelope detector has a probability-density function given by 9 

p s (R) dR=* exp (- X*±^)JM) dR (2 .27) 

Wo ^ 2ip Q / \ip / 

where I (Z) is the modified Bessel function of zero order and argument Z, defined by 

/o(Z)= ,lo2^!7! 
For Z large, an asymptotic expansion for / (Z) is 

/„(Z) « -L= (l + —+■••) 

" JlirZ \ 8Z / 

When the signal is absent, A = and Eq. (2.27) reduces to Eq. (2.21), the probability- 
density function for noise alone. 

The probability that the signal will be detected (which is the probability of detection) 
is the same as the probability that the envelope R will exceed the predetermined threshold 
V T . The probability of detection P a is therefore 

Pa = (" Ps(R) dR = {" - exp (- X*±A)ljM) d R (2.28) 

Jv T ->v t y> \ 2rp I \y) ' 

This cannot be evaluated by simple means, and numerical techniques or a series 
approximation must be used. A series approximation valid when RA/y) > 1, 
A > \R — A\, and terms in A~ 3 and beyond can be neglected is 9 



-'('-" ^) 



(V T - Af 
expi-^ — 

_ 2fo_ 

72^0 ^ ' 2 N /277(/l/ x /t/ , o) 

X 



1 _ V t~ A .l. 1+(Vt- -4) 2 /Vu 



4A SA 2 /y> 



(2.29) 



where the error function is defined as 



2 C z * 
erfZ = -^ e~ u du 



L [ z 

A graphic illustration of the process of threshold detection is shown in Fig. 2.6. The 
probability density for noise alone [Eq. (2.21)] is plotted along with that for signal and 
noise [Eq. (2.27)] with Ajip\ = 3. A threshold voltage V T \\f\ = 2.5 is shown. The 
crosshatched area to the right of V T \\p\ under the curve for signal-plus-noise represents 
the probability of detection, while the double-crosshatched area under the curve for 
noise alone represents the probability of a false alarm. If V T \y\ is increased to reduce 
the probability of a false alarm, the probability of detection will be reduced also. 

Equation (2.29) may be used to plot a family of curves relating the probability of 
detection to the threshold voltage and to the amplitude of the sine-wave signal. Al- 
though the receiver designer prefers to operate with voltages, it is more convenient for 
the radar system engineer to employ power relationships. Equation (2.29) may be 
converted to power by replacing the signal-to-rms-noise-voltage ratio with the follow- 
ing: 

A _ signal amplitude _ V2(rms signal voltage) _ / ? signal power V _ /2S^ 
fl rms noise voltage rms noise voltage \ noise power/ \N 1 



34 Introduction to Radar Systems 



[Sec. 2.5 



0.6 


Noise alone 


C.5 


~ 1 \ Threshold 


0.4 
0.3 


-/ \ l/77-^Signol + noise 

J \ /%yy>K (^ 2 = 3) 


0.2 




0.1 







— *x.... i w$4<ZY///fr>>. i i 



We shall also replace Ff./2y by In (1/P fa ) [from 
Eq. (2.24)]. Using the above relationships, the 
probability of detection is plotted in Fig. 2.7 as 
a function of the signal-to-noise ratio with the 
probability of a false alarm as a parameter. 

Both the false-alarm time and the detection 
probability are specified by the system require- 
ments. The radar designer computes the prob- 
ability of the false alarm and from Fig. 2.7 
determines the signal-to-noise ratio . This is the 
signal-to-noise ratio that is used in the equation 
for minimum detectable signal [Eq. (2.6)]. The 
signal-to-noise ratios of Fig. 2.7 apply to a single 
radar pulse. For example, suppose that the 
desired false-alarm time was 1 5 min and the IF 

bandwidth was 1 Mc. Thisgivesafalse-alarmprobabilityofl.il X 10~ 9 . Figure 2.7 

indicates that a signal-to-noise ratio of 13.1 db is required to yield a 0.50 probability 

of detection, 14.7 db for 0.90, and 16.5 db for 0.999. 
There are several interesting facts illustrated by Fig. 2.7. At first glance, it might 

seem that the signal-to-noise ratio required for detection is higher than that dictated by 



2*3 



5 6 
Wo" 



Fig. 2.6. Probability-density functions for 
noise alone and for signal-plus-noise, illus- 
trating the process of threshold detection. 



0.9999 

0.9995 
0.999 
0.998 

0.995 
0.99 
0.98 

.1 0.95 
« 0.90 

"D 
O 

I" 0.80 

1 0.70 
0.60 
0.50 
0.40 
0.30 

0.20 

0.10 
0.05 




10 I0 io 'icr 12 

1 I I L 



false alarm 



10 12 14 

(V/yl), signal-to-noise ratio, db 



16 



18 



20 



Fig. 2.7. Probability of detection for a sine wave in noise as a function of the signal-to-noise (power) 
ratio and the probability of false alarm. 



Sec. 2.6] The Radar Equation 35 

intuition, even for a probability of detection of 0.50. One might be inclined to say that 
so long as the signal is greater than noise, detection should be accomplished. Such 
reasoning may not be correct when the false-alarm probability is properly taken into 
account. Another interesting effect to be noted from Fig. 2.7 is that a change of only 
3.4 db can mean the difference between reliable detection (0.999) and marginal detection 
(0.50). Also, the signal-to-noise ratio required for detection is not a sensitive function 
of the false-alarm time. For example, a radar with a 1-Mc bandwidth requires a 
signal-to-noise ratio of 14.7 db for a 0.90 probability of detection and a 15-min false- 
alarm time. If the false-alarm time were increased from 1 5 min to 24 hr, the signal-to- 
noise ratio would be increased to 15.4 db. If the false-alarm time were as high as I 
year, the required signal-to-noise ratio would be 16.2 db. 

2.6. Integration of Radar Pulses 

The relationship between the signal-to-noise ratio, the probability of detection, and 
the probability of false alarm as given in Fig. 2.7 applies for a single pulse only. How- 
ever, many pulses are usually returned from any particular target on each radar scan 
and can be used to improve detection. The number of pulses n B returned from a point 
target as the radar antenna scans through its beamwidth is 

n n = -4lr=Mr ( 2.30) 

where d B = antenna beamwidth, deg 

f r = pulse repetition frequency, cps 
0, = antenna scanning rate, deg/sec 
(o m = antenna scan rate, rpm 
Typical parameters for a ground-based search radar might be pulse repetition frequency 
300 cps, 1.5° beamwidth, and antenna scan rate 5 rpm (30°/sec). These parameters 
result in 1 5 hits from a point target on each scan. The process of summing all the radar 
echo pulses for the purpose of improving detection is called integration. Many 
techniques might be employed for accomplishing integration, as discussed in Sees. 9.8 
and 9.9. All practical integration techniques employ some sort of storage device. 
Perhaps the most common radar integration method is the cathode-ray-tube display 
combined with the integrating properties of the eye and brain of the radar operator. 
The discussion in this section is concerned primarily with integration performed by elec- 
tronic devices in which detection is made automatically on the basis of a threshold 
crossing. 

Integration may be accomplished in the radar receiver either before the second 
detector (in the IF) or after the second detector (in the video). A definite distinction 
must be made between these two cases. Integration before the detector is called 
predetection, or coherent, integration, while integration after the detector is called 
postdetection, or noncoherent, integration. An example of a predetection integrator 
is a narrowband IF filter with a bandwidth approximately equal to the reciprocal of 
the time on target. (The storage device in this instance is the inductance and capacitance 
constituting the narrowband resonant network.) If, for example, the time on target 
were 0.05 sec, the bandwidth of the IF predetection filter would be approximately 20 
cps. This is rather small compared with that of a receiver designed to optimize the 
signal-to-noise ratio of a single pulse (which is of the order of a megacycle or so for 
radars with pulse widths in the vicinity of 1 //sec). Predetection integration requires 
that the phase of the echo signal be preserved if full benefit is to be obtained from the 
summing process. On the other hand, phase information is destroyed by the second 
detector; hence postdetection integration is not concerned with preserving RF phase. 



36 Introduction to Radar Systems [Sec. 2.6 

For this convenience, postdetection integration is not as efficient as predetection 
integration. 

If n pulses, all of the same signal-to-noise ratio, were integrated by an ideal pre- 
detection integrator, the resultant, or integrated, signal-to-noise (power) ratio would be 
exactly n times that of a single pulse. If the same n pulses were integrated by an ideal 
postdetection device, the resultant signal-to-noise ratio would be less than n times that 
of a single pulse. This loss in integration efficiency is caused by the nonlinear action of 
the second detector, which converts some of the signal energy to noise energy in the 
rectification process. The simplest form of postdetection integrator might consist of a 
low- pass filter made up of a resistor and a capacitor in the video portion of the receiver. 
Because of spectrum foldover produced by the second detector, the bandwidth of the 
low-pass filter should be about one-half the bandwidth of the predetection filter that 
integrates the same number of pulses. The IF filter used ahead of a video postdetection 
integrator should be the matched filter designed for a single pulse. 

In general, postdetection integration is easier to implement than predetection 
integration. It is an easier task to obtain a narrowband, low-pass video filter consisting 
simply of a capacitor and a resistor than it is to obtain a narrowband IF filter, or more 
precisely, a comb filter. The Q of an IF predetection filter would have to be large, and 
instability of the transmitter frequency might make it difficult to maintain the frequency 
of the echo signal within the narrowband IF filter. In addition, the predetection 
integrator requires that the phase of the RF or IF carrier oscillations be maintained 
coherent over a time corresponding to the time on target. By coherent it is meant that 
the phase of the received signal must remain constant with respect to the phase of the 
transmitted signal. The design of the predetection integrator is further complicated if 
the target is in motion and produces a doppler-shifted echo that lies outside the passband 
of the integrator. To circumvent this, a number of similar integrators, each tuned to a 
slightly different frequency, can be used to cover the frequency region in which echo 
signals are expected. 

The comparison of predetection and postdetection integration may be briefly 
summarized by stating that although postdetection integration is not as efficient as 
predetection integration, it is easier to implement in most applications. Postdetection 
integration is therefore preferred, even though the integrated signal-to-noise ratio may 
not be as great. 

The efficiency of postdetection integration relative to ideal predetection integration 
has been computed by Marcum 10 when all pulses are of equal amplitude. The integra- 
tion efficiency may be defined as follows : 

£,(„) = iMk (2 .3,) 

n(S/N) H 

where n = number of pulses integrated 
(SjN^ = value of signal-to-noise ratio of a single pulse required to produce given 

probability of detection (for n = 1) 
(S/N)„ = value of signal-to-noise ratio per pulse required to produce same probability 

of detection when n pulses are integrated 
The improvement in the signal-to-noise ratio when n pulses are integrated postdetection 
is nE t (ri) and is the integration-improvement factor. The improvement with ideal 
predetection integration would be equal to n. Examples of the postdetection integra- 
tion-improvement factor l ( (n) = nE t (ji) are shown in Fig. 2.8o. These curves were 
derived from data given by Marcum. The integration loss is shown in Fig. 2.86, 
where integration loss in decibels is defined as L t (n) = 10 log 10 [l/E^ri)]. The integra- 
tion-improvement factor (or the integration loss) is not a sensitive function of either the 
probability of detection or the probability of false alarm. 



Sec. 2.6] 

1,000 



The Radar Equation 37 



100 — 



10 — 



I I I I I I I l| I I I f I I M| 


i i i ii 1 1/| i i i i 1 1 if 


- 






stg&^Pd =0.90^=10* s' - 
^0><Pd-O5o/ ^ - 






I 


Zz^s -^ 


— 


/%?/ ^ 




^ / 
^ s- 


— 


J&r ^ 




~ JT ' 


- 


Jr •*" 




y^ ^ 




s\^ i [ 




*■ i i i i 1 1 1 il I 


I i i i i i i 1 1 i i i i i i i i 



10 100 1,000 

n, number of pulses integrated (postdetection) 

(a) 



10,000 




I I I I III I I l ll I I ll l I l l l l l ll i l l l I l l i I 

10 100 1,000 10,000 

n = number of pulses 

(A) 
Fig. 2.8. (a) Integration-improvement factor, square-law detector, P d = probability of detection, 
n f = false-alarm number; (b) integration loss as a function of n, the number of pulses integrated, P d , 
and n f . (After Marcum, 10 courtesy IRE Trans.) 



38 Introduction to Radar Systems [Sec. 2.6 

Also plotted in Fig. 2.8a are two straight lines representing the improvement that 
would be expected if the integration-improvement factor were equal to n and to «-, 
respectively. An improvement factor proportional to n applies to the ideal pre- 
detection integrator. It is hardly ever achieved in practice. An improvement factor 
proportional to n h fits the experimental data found with an operator viewing a cathode- 
ray-tube display (Sec. 9.7). When only a small number of hits are integrated post- 
detection (large signal-to-noise ratio per pulse), the integration-improvement factor is 
not much different from that which would be obtained from a perfect predetection 
integrator. On the other hand, when a large number of hits are integrated (small 
signal-to-noise ratio per pulse), the difference between the postdetection and pre- 
detection integration is more pronounced. The slope of the postdetection integration- 
improvement curve approaches the slope of the n k curve for n large. If the operator 
performance were actually that specified by the n l - curve, proper implementation of 
automatic postdetection integration could offer an improvement in detection capability 
over that of an operator. 

Figure 2.7 relates for a single pulse (n = 1) the signal-to-noise ratio to the probability 
of detection and the probability of false alarm. It may be used to determine the 
required signal-to-noise ratio per pulse (S/N) n at the output of the IF amplifier when n 
pulses are integrated, by applying the following procedure .: 

1. For the specified average false-alarm time Tt&, receiver bandwidth B, and 
number of pulses integrated n, compute the false-alarm probability Pf a = n/TtaB, or 
p {a = nlTta,f r f], where f r is the pulse repetition frequency and rj is the number of pulse 
intervals per radar sweep, or pulse-repetition period. 

2. For the desired probability of detection and probability of false alarm as com- 
puted above, enter Fig. 2.7 to find the signal-to-noise ratio (S/AOi for single-pulse 
detection. 

3. For the desired probability of detection P d , number of pulses integrated n, and 
false-alarm number n, = njPu = T ta B, find the integration-improvement factor 
nEf(n) from Fig. 2.8cr. 

4. Divide the signal-to-noise ratio (S/N\ found from step 2 by the integration- 
improvement factor nE t (ri) to obtain the signal-to-noise ratio per pulse (S/N) n required 
at the output of the IF amplifier for the specified P d and Pf a . 

The radar equation (2.7) taking account of integration may be written 

o-4 = P t GA e anE t {n) (2 3 „ 

maX {^fkT B n F n {SIN\ 

Exponential Weighting. Most practical integration techniques do not sum the echo 
pulses with equal weight as assumed above. Practical integrators such as the RC 
low-pass filter, the RLC resonant circuit, the recirculating-delay-line integrator, and 
the electrostatic storage tube apply an exponential weighting factor to the integrated 
pulses; that is, if n pulses are integrated, the voltage out of the integrator is 

V= 2 K 4 exp [-(n-i>] (2.33) 

i = \ 

where V i = voltage amplitude of i'th pulse 

exp (— y) = attenuation factor per pulse 
Consider a train of n pulses, where the nth pulse refers to the pulse stored the longest. 
Pulse 1, the last pulse to be received, is given a weight of unity, pulse 2 is attenuated by 
a factor e~ y , pulse 3 is attenuated by e~ 2,/ , and the Kth pulse is attenuated by e~ in ~ 1)v . In 
an RC low-pass filter y = TjRC, where 7 is the pulse-repetition period and RC is the 
filter time constant. In a narrowband RLC resonant circuit, y = niL/cy/R. In a 



Sec. 2.6] 



The Radar Equation 



39 



recirculating-delay-line integrator, e~ v is the attenuation around the loop (loop gain); 
and in the electrostatic storage tube, y is a factor describing the tube operation. 

Exponential weighting of the pulses results in less efficient integration than uniform 
weighting. (The optimum weighting function in a radar system would be one which 
duplicates the antenna scan envelope.) The efficiency depends upon the number of 
pulses integrated, the weighting factor, and whether the contents stored in the integrator 
are erased ("dumped") after n pulses or whether the integrator operates continuously 
without dumping. An integrator with dumping might be used with a step-scan radar. 
(In the step-scan radar, the antenna remains stationary until n pulses are transmitted 
and received, after which it is discontinuously stepped to the next position.) If dumping 




ny 



Fig. 2.9. Efficiency of an exponential integrator as a function of ny, where n = number of pulses and 
e~y is the attenuation factor per pulse (y is assumed small). 

were used in a continuous-scan radar, some targets might only be seen with half the 
number of hits. An example of an integrator that dumps is an electrostatic storage 
tube that is erased whenever it is read. Another example is a capacitor that is dis- 
charged on read-out. 

The weighting integration efficiency p is defined as the ratio of the integration- 
improvement factor with exponential weighting to that with uniform weighting. For 
a dumped integrator the efficiency is 12 

= tanh (ny/2) (2 34) 

n tanh (y/2) 

This is plotted in Fig. 2.9. As long as ny is less than unity, the exponential integrator 
with dumping is almost as efficient as the integrator with uniform weighting. The 
efficiency given by Eq. (2.34) was derived by comparing the average signal-to-noise ratio 
for the exponential integrator to the average signal-to-noise ratio for the uniform 
integrator, rather than by comparing the probability of detections as was done in the 
case of the integration-improvement factor described by Fig. 2.8a. 

The dumped integrator is not the general rule in practice, since there are few applica- 
tions besides the step-scan radar where it is known beforehand when the integrator is 
ready to be dumped of its contents. In most cases, the integrator is operated contin- 
uously. In the dumped integrator values of y ->■ are best, but this is not optimum 
with the continuous integrator. When y = 0, noise in the continuous integrator 
builds up to an "infinite" value and detection of signals is not possible. This corre- 
sponds to oscillation in the delay-line integrator, or to a zero bandwidth and a vanishing 



40 Introduction to Radar Systems [Sec. 2.7 

small output in the RC and RLC integrators, and to zero read-out in the electrostatic 
tube. 
The efficiency of the continuous exponential-weighting integrator may be shown to be 

l-exp(- H y) 
H [n tanh (y/2)]* K ' 

A plot of this equation is also shown in Fig. 2.9. For y small, tanh (y/2) is replaced by 
y/2. The maximum efficiency occurs for a value of ny = 1.257. If the number of 
pulses to be integrated is known beforehand, the value of y that maximizes the efficiency 
may be determined, and the optimum bandwidth of an integrating filter, or the loop 
gain of a delay-line integrator, may be found. 

2.7. Radar Cross Section of Targets 

The radar cross section of a target is the area intercepting that amount of power 
which, when scattered equally in all directions, produces an echo at the radar equal to 
that from the target; or in other terms, 



power reflected toward source/unit solid angle ,. „ , 

" : — — ; : — ; — = hm 4m Rr 

incident power density/477 r^ x 



(2.36) 



where R = distance between radar and target 

E r = reflected field strength 

Ef = strength of incident field 
For most common types of radar targets such as aircraft, ships, and terrain, the cross 
section does not bear a simple relationship to the physical area, except that the larger 
the target size, the larger the cross section is likely to be. 

When an object is illuminated by an electromagnetic wave, a portion of the incident 
energy is absorbed as heat and the remainder is reradiated (scattered) in many different 
directions. The portion of the reradiated energy scattered or reflected in the back or 
rearward direction is of chief interest in radar. In some cases, however, the energy 
scattered in other directions may also be important, as with a bistatic or CW wave- 
interference radar, where the receiver is not at the same location as the transmitter 
(Sec. 13.6). In the present section we shall be concerned only with the backscatter 
cross section. 

Scattering and diffraction are variations of the same physical process. 13 When an 
object scatters an electromagnetic wave, the scattered field is defined as the difference 
between the total field in the presence of the object and the field that would exist if the 
object were absent (but with the sources unchanged). On the other hand, the diffracted 
field is the total field in the presence of the object. With radar backscatter, the two 
fields are the same, and one may talk about scattering and diffraction interchangeably. 
In the case of forward scattering in bistatic radar, the scattered field -and the diffracted 
field could be quite different. 

In theory, the scattered field, and hence the radar cross section, can be determined by 
solving Maxwell's equations with the proper boundary conditions applied. 14 Un- 
fortunately, the determination of the radar cross section with Maxwell's equations can 
be accomplished only for the most simple of shapes, and solutions valid over a large 
range of frequencies are not easy to obtain. The radar cross section of a simple sphere 
target is shown in Fig. 2.10 as a function of its circumference measured in wavelengths 
(27Tfl/A, where a is the radius of the sphere and A is the wavelength). 15 The region where 
the size of the sphere is small compared with the wavelength {l-najl < 1) is called the 
Rayleigh region, after Lord Rayleigh, who, in the early 1 870s, first studied scattering by 
small particles. Lord Rayleigh was interested in the scattering of light by microscopic 



Sec. 2.7] 



The Radar Equation 41 



particles, rather than in radar. His work preceded the orginal electromagnetic echo 
experiments of Hertz by about fifteen years. The Rayleigh scattering region is of 
interest to the radar engineer because the cross sections of raindrops and other meteoro- 
logical particles fall within this region at the usual radar frequencies. Since the cross 
section of objects within the Rayleigh region varies as A -4 , rain and clouds are essentially 
invisible to radars which operate at relatively long wavelengths (low frequencies). The 
usual radar targets are much larger than raindrops or cloud particles, and lowering 
the radar frequency to the point where rain or cloud echoes are negligibly small will not 
seriously reduce the cross section of the larger desired targets. On the other hand, if it 
were desired to actually observe, rather than eliminate, raindrop echoes, as in a meteoro- 
logical or weather-observing radar, the higher radar frequencies would be preferred 
(Sec. 12.7). 



10p 



n — i — i i i i i i 



-i — i — r 




0.001 



I I 1 1 



0.3 0.4 0.5 0.8 1.0 2 

Circumference /wavelength 



3 4 5 6 
2-na/X 



20 



Fig. 2.10. Radar cross section of the sphere, a = radius; A = wavelength. 

At the other extreme from the Rayleigh region is the optical region, where the dimen- 
sions of the sphere are large compared with the wavelength {2-irajX > 1). For large 
2-na\l, the radar cross section approaches the optical cross section tto 2 . In between the 
optical and the Rayleigh region is the Mie, or resonance, region. The cross section is 
oscillatory with frequency within this region. The maximum value reached is 5.7 db 
greater than the optical value, while the minimum value, excluding the Rayleigh region, 
where the cross section goes to zero in the limit of infinite wavelength, is 4 db below the 
optical. (The theoretical values of the maxima and minima may vary according to 
the method of calculation employed. 15 ) The behavior of the radar cross sections of 
other simple reflecting objects as a function of frequency is similar to that 
of the sphere. 13 ' 1416 - 21 

Since the sphere is a sphere no matter from what aspect it is viewed, its cross section 
will not be aspect-sensitive. The cross section of other objects, however, will depend 
upon the direction as viewed by the radar. Figure 2.11 shows the experimentally 
measured backscatter (radar) cross section for a right-circular cone as a function of 
aspect. 22 Three different sizes of cones are shown, each with an apex angle of 1 5°. 
The diameter of the base of the large cone is 2A, that of the intermediate cone A, and that 
of the small cone 2/2. The radar is assumed to be in the same plane as the axis of the 



42 Introduction to Radar Systems 

12 



[Sec. 2.7 



£ -12 



-16 




160 



180 



60 80 100 120 

Aspect angle , deg 

Fig. 2.11. Experimentally measured backscatter cross section for a right-circular cone as a function 
of aspect, a, relative to a 4.75A-diameter sphere. (1) Large cone (base diameter 2A); (2) intermediate 
cone (base diameter A); (3) small cone (base diameter A/2). {From Shostak and Angelakos. 22 ) 



T 




Measured 

Calculated 




Fig. 2.12. 



20 30 40 50 60 70 80 90 

Angular orientation 8 

Backscatter cross section of a long thin rod. (From Peters, 23 IRE Trans.) 



cone, and the polarization is perpendicular to the plane containing the cone axis and the 
line of sight (vertical polarization). The abscissa is the aspect angle. The angle 
6 = 0° corresponds to viewing the base of the cone, and = 180°, the apex of the cone. 
The ordinate is the radar cross section relative to a sphere with a diameter of 4.751 
(Measurements were made at a frequency of 9,346 Mc.) 



The Radar Equation 



43 



Sec. 2.7] 

Figure 2. 1 2 is a plot of the backscatter cross section of a long thin rod as a function of 
aspect. 23 The rod is 39A long and A/4 in diameter and is made of silver. Both theoreti- 
cal and measured data are shown. If the rod were of steel instead of silver, the first 
maximum would be about 5 db below that shown. The radar cross section of the ogive 
shown in Fig. 2.13a is plotted in.Fig. 2.136. 23 In both Figs. 2.12 and 2.13, the plane of 
polarization is perpendicular to the line of sight but is in the same plane as the longi- 
tudinal axis of the object (horizontal polarization). 

The cross sections of some typical simple scattering objects for particular aspects are 
tabulated in Table 2.2. 13 These are valid if the dimensions of the object are large 



Table 2.2. Formulas for Radar Cross Sections of Scatterers of Large 
Characteristic DiMENSiONst 



Scatterer 


Aspect 


Radar cross section 


Definition of symbols 






a = 7ra 2 




a = radius 




Axial 


A 2 
a = tt- tan 4 o 




6 = cone half angle 


Paraboloid 


Axial 


107T 

a = A^l 




2£o = apex radius of 
curvature 


Prolate spheroid 


Axial 


<r-— ° 
a l 




a = semimajor axis 
b = semiminor axis 




Axial 


a = rz~ tan * o 




0„ = half angle of target 


Circular plate . . . 


Incidence at angle 
to normal 


\6n 

„ /47TO . 

a = na 2 cot 2 6 Jl\-j- sir 


») 


a = radius of plate 


Large flat plate of 
arbitrary shape 


Normal 


4t7/4 2 




A = plate area 


Circular cylinder 


Incidence at angle 
6 to broadside 


al cos 6 sin 2 (kL sin 
" ~ 1-n sin 2 6 


6) 


a = radius 

L = cylinder length 



t Mentzer. 11 



compared with the wavelength. When the radius of curvature of the reflecting surface 
is large compared with the wavelength, the methods of geometrical optics may be 
applied to compute the radar cross section. The geometrical-optics cross section is 

a = TrRyRz 

where i?j and R 2 are the two principal radii of curvature with respect to two orthogonal 
curvilinear coordinate directions on the surface. In the case of the sphere, R l =R 2 = a, 
where a is the radius ; thus a = 77a 2 . 

The cross sections of simple scattering objects are of interest not only because of the 
insight they give to the scattering properties of more complex radar targets such as 
aircraft, ships, and surface objects, but they are characteristic of such important 
targets as meteorological objects (rain, snow, ice) and certain classes of space objects. 

Complex Targets. The radar cross section of complex targets such as ships, aircraft, 
cities, and terrain are complicated functions of the viewing aspect and the radar fre- 
quency. Target cross sections may be computed with the aid of digital computers, or 
they may be measured experimentally. The target cross section can be measured with 
full-scale targets, but it is more convenient to make cross-section measurements on scale 



44 Introduction to Radar Systems [Sec. 2.7 

models at the proper scaled frequency. Most radar cross-section information con- 
cerning complex targets is obtained in this manner. The theoretical computation of 
target cross section was pioneered and developed by Siegel and associates at the Univer- 
sity of Michigan Radiation Laboratory. 24 

A complex target may be considered as comprising a large number of independent 
objects that scatter energy in all directions. The energy scattered in the direction of the 
radar is of prime interest. The relative phases and amplitudes of the echo signals from 




31.0 



Measured 
: Points calculated by optics 
Calculated curve due to traveling waves 
Calculated maxima due to traveling waves 




30 40 50 60 

Angular orientation 

[6) 
Fig. 2.13. (a) Dimensional drawing of the ogive; (6) backscatter cross section of the ogive. (From 
Peters, 23 IRE Trans.) 

the individual scattering objects as measured at the radar receiver determine the total 
cross section. The phases and amplitudes of the individual signals might add to give a 
large total cross section, or the relationships with one another might result in total 
cancellation. In general, the behavior is somewhere between total reinforcement and 
total cancellation. If the separation between the individual scattering objects is large 
compared with the wavelength— and this is usually true for most radar applications— 
the phases of the individual signals at the radar receiver will vary as the viewing aspect is 
changed and cause a scintillating echo. 

Consider the scattering from a relatively "simple" complex target consisting of two 



Sphere f* 
target " 



Sphere 
target 



Sec. 2.7] The Radar Equation 45 

equal, isotropic objects (such as spheres) separated a distance / (Fig. 2.14). By iso- 
tropic scattering is meant that the radar cross section of each object is independent of 
the viewing aspect. The separation / is assumed to be less than ct/2, where c is the 
velocity of propagation and r is the pulse duration. 
With this assumption, both scatterers are illuminated 
simultaneously by the pulse packet. Another restric- 
tion placed on / is that it be small compared with the 
distance R from radar to target. Furthermore, R x on 
R 2 as R, The cross sections of the two targets are 
assumed equal and are designated a . The RF voltage 
received at the radar from each target of cross section a 
is proportional to 

- AttR, 



V t = Kyja cos -^ V 2 = Kjo cos 




Radar 



Fig. 2.14. Geometry of the two- 
where K is a constant which includes the parameters scatterer complex target, 
involved in the radar equation. The echo signals from 

the two reflecting objects add vectorially. The resultant signal depends upon the 
phase of each echo signal as well as the amplitude. The resultant voltage from the 
two objects is 



V r = Ksjo^cos, 
by trigonometry : 



— \R sin 6 1 

Lav 2 /J 



cos 



A + B 
cos A + cos B = 2 cos cos 



- sin 

2 



')]) 



B 



so that 



where 



or 



V r = Kjo 



4nR 

2 cos cos 



a r = 4<r cos s 



£r = 2 



1 + cos 






„ I— 4 " R 

= KJa, cos 

V A 



(2.37) 



(2.38) 



The ratio aJa Q can be anything from a minimum of zero to a maximum of four times the 
cross section of an individual scatterer. Polar plots of cr r /cr for various values of //A are 
shown in Fig. 2. 1 5. Although this is a rather simple example of a "complex" target, it 
is complicated enough to indicate the type of behavior to be expected with practical 
radar targets. 

The radar cross sections of actual targets are far more complicated in structure than 
the simple two-scatterer target. Practical targets are composed of many individual 
scatterers, each with different scattering properties. Also, interactions may occur 
between the scatterers which affect the resultant cross section. 

An example of the cross section as a function of aspect angle for a propeller-driven 
aircraft 25 is shown in Fig. 2.16. The aircraft is the B-26, a World War II medium-range 
two-engine bomber. The radar wavelength was 10 cm. These data were obtained 
experimentally by mounting the aircraft on a turntable in surroundings free from other 
reflecting objects and by observing with a nearby radar set. The propellers were 
running during the measurement and produced a modulation of the order of 1 to 2 kc. 



46 Introduction to Radar Systems 



[Sec. 2.7 



2 3 4 -9°° 





-90° 




3 4 -90° 



U-4A-J 



Fig. 2. 1 5. Polar plots of <t t /ct for the two-scatterer complex target [Eq. (2.38)]. (a) / = A ; (£>) / = 2A ; 
(c) / = 4A. 

The cross section can change by as much as 1 5 db for a change in aspect of only |°. 
The maximum echo signal occurs in the vicinity of broadside, where the projected area 
of the aircraft is largest. 

Figure 2.17 compares the theoretical and experimental cross section of the B-47 
bomber aircraft as a function of aspect angle and frequency. The theoretical data 
(solid curves) represent averages over a limited aspect angle; the fine structure is not 
included. The accuracy of theoretical cross sections is claimed to be from 2 to 10 db. 
Experimental-measurement accuracies also are of the same order of magnitude. The 
frequency dependence is seen to be slight. 

Siegel's cross-section-computation technique lends itself quite well to the analysis of 
the relative contribution of various target components to the over-all cross 



Sec. 2.7] 



The Radar Equation 47 



35db 




Fig. 2.16. Experimental cross section of the B-26 two-engine bomber at 10-cm wavelength as a 
function of azimuth angle. {From Ridenour, u courtesy McGraw-Hill Book Company, Inc.) 



University of Michigan 330Mc 
Evans Signal Laboratory !50Mc 
Ohio State University 195 Mc 
— Radiation, Inc. 600 Mc 




20 



40 



60 



80 100 

Azimuth, deg 



120 



140 160 



180 



Fig. 2.17. Comparison of the theoretical and experimental cross section of the B-47 jet aircraft as a 
function of aspect and frequency as obtained by various investigators. (Courtesy K. Siegel, University 
of Michigan.) 



48 



Introduction to Radar Systems 



[Sec. 2.7 



10' 



10' 



10' 



10° 



to- -\ 



10"' 



10" 





I ! I I 

X 

it A 


1 


- 


J 


/ A 


Trailing edge ~~ 




.^ 


/ \ 


of stabilizer-^ 




s 


Leading 1 \-rv 




^ 


edge of 1 \ ^. 




1 






stabilizer 1 J V5 


.& 


1 


- 


^ i 


/ / J\\ 





/ " 




■§ 


/ 7 A \ \ 


<b 


/ 






/ /A\ \ 










/ Jf\\ \ 


M 






y n \ 

// \ 






-\ 


, 
























1 


1 1 1 


T ' 


— ' ' — L"*« 



Azimuth angle, deg off nose-on aspect 

Fig. 2.18. Radar cross section of the components of a typical large manned jet aircraft at a wavelength 
of 0.71 m. (Courtesy K. Siegel, University of Michigan) 




0.691 0.695 0.699 



0.703 0.707 0.711 
A, meters 



0.715 0.719 0.723 



Fig. 2.19. Cross section as a function of wavelength for the nose-on aspect of a large jet aircraft. 
(Courtesy K. Siegel, University of Michigan.) 

section. The effect of the various components is shown in Fig. 2. 1 8 for a typical large 
manned jet aircraft. 24 There are many significant contributors to be considered, but 
no single component dominates over the entire range of aspect angles. The variation 
of the cross section as a function of wavelength for the nose-on aspect is shown in Fig. 
2.19. 
The radar cross sections presented above apply for horizontal polarization. Most 



Sec. 2.7] 



The Radar Equation 49 



search radars whose prime targets are aircraft usually employ this type of polarization. 
If vertical or some other polarization is used, the cross sections may be different. An 
example of the difference between horizontal and vertical polarization is shown in Fig. 
2.20. The radar scattering properties of a target for any polarization may be described 
by a 2 x 2 matrix of <r's corresponding to transmitting each of two orthogonal polari- 
zations and receiving with the same polarization or the orthogonal polarization. This 
is known as the polarization scattering matrix. 13 - 26 " 28 

Most cross-section data, either theoretical or experimental, assume the target to have 
a smooth reflecting surface. Apparently considerable surface roughness can be 
tolerated before a significant effect on the value of cross section is obtained. It has been 
reported 29 that the roughness depth of a sphere's surface can be as large as 0.01 A without 
causing a change in cross section of more than 0. 1 db. The "roughness" to which this 
statement applies are surface irregularities distributed at random, but in a statistically 
uniform and isotropic manner. The surface slopes are assumed small, and the mini- 
mum radius of curvature of the mean (unperturbed) surface is assumed large compared 
with the wavelength. 

Radar cross sections can be considerably reduced by properly shaping the target or by 
coatings that absorb, rather than reflect, electromagnetic energy (Sec. 12.10). How- 
ever, absorbing materials have little effect on the radar cross section when (1) the radar 
wavelength is large compared with the target dimensions (Rayleigh scattering) 30 or 
(2) the target is observed by a forward scatter (bistatic) radar whose wavelength is small 
compared with the target dimensions. 31 

The measured radar cross section of a man has been reported 32 to be as follows : 



uency, Mc 


a, m 2 


410 


0.033-2.33 


1,120 


0.098-0.997 


2,890 


0.140-1.05 


4,800 


0.368-1.88 


9,375 


0.495-1.22 



50 



40 



= 30- 



T3 20 ■ 



10 



... J „ 1 






i 




i i 






M 

A "f 
It ii 

ml 


In 

i | 


/ \ 




1 1 




vliil 

IHl 


j 








1 


in / 1 


• /> J 

\ ' \ In 

v/ \ J 


''HI 
i ill 

/ lJU 

i 






\K- ^~ 


i / 














































polarization 














1 1 




i 


i 




polarizotion 

1 1 



20 40 60 80 100 120 140 160 180 

Aspect angle, deq measured from nose-on in plane of wing 

Fig. 2.20. Experimental cross sections for a large aircraft at approximately 75 Mc as a function of 
polarization and aspect. (Courtesy K. Siegel, University of Michigan) 



50 Introduction to Radar Systems [Sec. 2.8 

The spread in cross-section values represents the variation with aspect and polarization. 
The cross-section data presented in this section lead to the conclusion that it would 
not be appropriate to simply select a single value and expect it to have meaning in the 
computation of the radar equation without further qualification. Methods for dealing 
with the cross sections of complicated targets are discussed in the next section. 

2.8. Cross-section Fluctuations 

The discussion of the minimum signal-to-noise ratio in Sec. 2.6 assumed that the echo 
signal received from a particular target did not vary with time. In practice, however, 
the echo signal from a target in motion is almost never constant. Variations in the 
echo signal may be caused by meteorological conditions, the lobe structure of the 
antenna pattern, or equipment instabilities. But the chief source of fluctuation is that 
of variations in the target cross section. 



Time, sec —*■ 

Fig. 2.21. Pulse-by-pulse record of the echo signals from a Meteor jet aircraft flying toward the 
radar. {After Hay. 33 ) 

The cross sections of complex targets (the usual type of radar target) are quite 
sensitive to aspect. Therefore, as the target aspect changes relative to the radar, 
variations in the echo signal will result. A typical pulse-by-pulse record of the echo 
from a Meteor aircraft (British two-engine jet fighter) flying toward a radar is represented 
in Fig. 2.21 . Hay 33 reports that analyses of records of this type show that the period of 
the fluctuation varies from several seconds at long ranges to a few tenths of a second at 
short ranges. The fluctuation period also depends on radar wavelength. The degree 
of echo modulation for this target varies from 26 db to less than 10 db for different 
aspects of the aircraft. Similar effects occur for propeller-driven aircraft such as the 
B-26 (Fig. 2.16). 

One method of accounting for a fluctuating cross section in the radar equation is to 
select a lower bound, that is, a value of cross section that is exceeded some specified 
(large) fraction of time. The fraction of time that the actual cross section exceeds the 
selected value would be close to unity (0.95, 0.99, or 0.999 being typical). For all 
practical purposes the value selected is a minimum and the target will always present a 
cross section greater than that selected. This procedure results in a conservative pre- 
diction of radar range and has the advantage of simplicity. The minimum cross section 
of typical aircraft or missile targets generally occurs at or near the head-on aspect. 

However, to properly account for target cross-section fluctuations, the probability- 
density function and the correlation properties with time must be known for the 
particular target and type of trajectory. Curves of cross section as a function of aspect 
and a knowledge of the trajectory with respect to the radar are needed to obtain a true 
description of the dynamical variations of cross section. The probability-density 
function gives the probability of finding any particular value of target cross section 
between the values of a and a + da, while the autocorrelation function describes the 
degree of correlation of the cross section with time or number of pulses. The spectral 
density of the cross section (from which the autocorrelation function can be derived) is 
also sometimes of importance, especially in tracking radars. It is usually not practical 
to obtain the experimental data necessary to compute the probability-density function 



Sec. 2.8] The Radar Equation 51 

and the autocorrelation function from which the over-all radar performance is deter- 
mined. Most radar situations are of too complex a nature to warrant obtaining 
complete data. A more economical method to assess the effects of a fluctuating cross 
section is to postulate a reasonable model for the fluctuations and to analyze it 
mathematically. Swerling 34 has calculated the detection probabilities for four different 
fluctuation models of cross section. These typical situations bracket a wide range of 
practical cases. In two of the four cases, it is assumed tjiat the fluctuations are com- 
pletely correlated during a particular scan but are completely uncorrected from scan to 
scan. In the other two cases, the fluctuations are assumed to be more rapid and 
uncorrected pulse to pulse. The four fluctuation models are as follows : 

Case 1 . The echo pulses received from a target on any one scan are of constant 
amplitude throughout the entire scan but are independent (uncorrelated) from scan to 
scan. This assumption ignores the effect of the antenna beam shape on the echo 
amplitude. An echo fluctuation of this type will be referred to as scan-to-scan fluctua- 
tion. The probability-density function for the cross section a is given by the Rayleigh 
density function 

p(a) = — exp(- — ) <7>0 (2.39) 

where cr av is the average cross section over all target fluctuations. 

Case 2. The probability-density function for the target cross section is also given by 
Eq. (2.39), but the fluctuations are more rapid than in case 1 and are taken to be in- 
dependent from pulse to pulse instead of from scan to scan. 

Case 3. In this case, the fluctuation is assumed to be independent from scan to scan 
as in case 1 , but the probability-density function is given by 

p(<r) = ^exp(-^) (2.40) 

#av V O m l 

Case 4. The fluctuation is pulse to pulse according to Eq. (2.40). 

The Rayleigh probability-density function assumed in cases 1 and 2 applies to a 
target consisting of many independent fluctuating scatterers of approximately equal 
echoing areas. Although, in theory, the number of independent scatterers must be 
essentially infinite, in practice the number may be as few as four or five. Cross-section 
fluctuations of objects with dimensions large compared with a wavelength are also 
expected to approximately follow the Rayleigh probability-density function. The 
majority of radar targets are probably of this nature. The probability-density function 
assumed in cases 3 and 4 is more indicative of targets that can be represented as one large 
reflector together with other small reflectors, or as one large reflector subject to fairly 
small changes in orientation. In all the above cases, the value of cross section to be 
substituted in the radar equation is the average cross section a av . The signal-to-noise 
ratio needed to achieve a specified probability of detection without exceeding a specified 
false-alarm probability can be calculated for each model of target behavior. For 
purposes of comparison, the nonfluctuating cross section will be called case 5. 

A comparison of these five cases for a false-alarm number n f = 10®^ = n/Pfa) is 
shown in Fig. 2.22 for n = 10 hits integrated. When the detection probability is large, 
all four cases in which the target cross section is not constant require greater signal-to- 
noise ratio than the constant cross section of case 5. For example, if the desired 
probability of detection were 0.95, a signal-to-noise ratio of 6.2 db/pulse is necessary if 
the target cross section were constant (case 5), but if the target cross section fluctuated 
with a Rayleigh distribution and were scan to scan uncorrelated (case 1), the signal-to- 
noise ratio would have to be 16.8 db/pulse. This increase in signal-to-noise corre- 
sponds to a reductionin range by a factor of 3.28. Therefore, if the characteristics of the 



52 Introduction to Radar Systems [Sec. 2.8 

target cross section are not properly taken into account, the actual performance of the 
radar might not measure up to the performance predicted as if the target cross section 
were constant. Figure 2.22 also indicates that for probabilities of detection greater 
than about 0.30, a greater signal-to-noise ratio is required when the fluctuations are 
uncorrelated scan to scan (cases 1 and 3) than when the fluctuations are uncorrelated 
pulse to pulse (cases 2 and 4). In fact, the larger the number of pulses integrated, the 
more likely it will be for the fluctuations to average out, and cases 2 and 4 will approach 
the nonfluctuating case. This does not occur when the cross section is assumed to be 
constant throughout a particular scan of n pulses. In the region where the signal-to- 
noise ratio required for a given detection probability is greater for the nonfluctuating 



0.99 


- 


I I 


I I 
5 4 2 


I I 
,3 


I 


0.98 








/ 1 


- 


0.95 










- 


0.90 










- 


<£"0.80 










- 


.1 0.70 
2 0.60 

1-0.40 
I 0.30 

o 

S 0.20 
a. 


- 








- 


0.10 










- 


0.05 










- 


0.02 


- 








- 


0.01 


- 




I I 


i l 


i 



-10 



5 10 15 20 

Signal-to-noise ratio per pulse, db 



25 



30 



Fig. 2.22. Comparison of detection probabilities for five different models of target fluctuation for 
n = 10 pulses integrated and false-alarm number n, = 10 8 (n, = n/P fa ). (Adapted from Swerling." 1 ) 



case than for any of the four fluctuating cases, the detection probability is lower (<0.30) 
than would normally be considered useful for radar application and is of little practical 
interest. 

Swerling 34 computed the detection-probability characteristics for fluctuating targets 
as a function of P d , n f , n, and signal-to-noise ratio. The curves presented in Figs. 2.23 
and 2.24 were derived from his report. The data in these two figures, along with the 
detection-probability curves of Fig. 2.7, may be used to find the signal-to-noise ratio per 
pulse for any of the four fluctuating cases. The procedure is as follows : 

1. Find the signal-to-noise ratio from Fig. 2.7 corresponding to the desired value of 
detection probability P d and false-alarm probability Pt&. 

2. From Fig. 2.23 determine the correction factor for either cases 1 and 2 or cases 3 
and 4 to be applied to the signal-to-noise ratio found from step 1 above. The resultant 
signal-to-noise ratio (5/A') 1 is that which would apply if detection were based upon a 
single pulse. 

3. If n pulses are integrated, the signal-to-noise ratio found in step 2 for a single pulse 



Sec. 2.8] 



The Radar Equation 53 




001 005 0.1 0.2 0.3 0.5 0.7 0.8 0.9 0.95 0.99 

Probability of detection 

Fig. 2.23. Additional signal-to-noise ratio required to achieve a particular probability of detection, 
when the target cross section fluctuates, as compared with a nonfluctuating target; single hit, » = 1. 




10 20 50 100 

Number of pulses integrated, n 



500 1,000 



Fig. 2.24. Integration-improvement factor as a function of the number of pulses integrated for the 
five cases of target fluctuations considered. 



54 



Introduction to Radar Systems 



[Sec. 2.8 

is divided by the integration-improvement factor /<(«) = nE^ri) from Fig. 2.24 in order 
to find the signal-to-noise ratio per pulse. The parameters {SjN\ and nE { {n) are those 
substituted into the radar equation (2.32) along with cr av . 

The integration-improvement factor in Fig. 2.24 is in some cases greater than n, or in 
other words, the integration efficiency factor E^ri) > 1 . One is not getting something 
for nothing, for in those cases in \vhich the integration-improvement factor is greater 
than n, the signal-to-noise ratio required for « = 1 is larger than for a nonfluctuating 
target. The signal-to-noise per pulse will always be less than that of an ideal pre- 
detection integrator for reasonable values of P d . It should also be noted that the data 

0.999 
0.998 

0.995 
0.99 
0.98 

0.95 
c? 

c 0.90 
o 

I 0.80 

^ 0.70 

H °- 60 

1 °- 50 
1 0.40 

£ 0.30 
0.20 

0.10 
0.05 



- 


i i i i i 

/ 


III! 




No fluctuation ' 




— 


(constant signal J 
amplitude)-- 1 

7 







'y y /- ^^~y 


- 


! A 


y ^^ 


: 


1/^ 


- 


— 


i /? / 


— 


— 




- 


_ 


/ 1 


_ 


— 


/ i i i i 


-Jill 



10 12 14 16 18 20 22 

Mean signal-to-noise ratio per pulse, db 



24 



26 



Fig. 2.25. Effect of correlation between pulses on the detection probability; p = signal voltage 
correlation coefficient; square-law detector; Rayleigh fluctuation; two pulses integrated (n — 2). 
{After Schwartz, 35 courtesy IRE Trans.) 

in Figs. 2.23 and 2.24 are essentially independent of the false-alarm number, at least 
over the range of 10 6 to 10 10 . 

Partial Correlation. The fluctuation models considered above assume either com- 
plete correlation between the pulses in any particular scan (cases 1 and 3) or else 
complete independence between the pulses (cases 2 and 4). These represent two 
extreme cases of fluctuations. In general, it is likely that the pulses of a particular scan 
will lie within these two extremes and be partially correlated. 

Schwartz 35 considered the effect of partial correlation on the addition of two fluctuat- 
ing signals (n = 2). The signals are assumed to be correlated according to the correla- 
tion coefficient, 



(2.41) 



9 (<>!<#* 

where x lt x 2 = amplitudes of two successive pulses 

x lt x 2 = mean values (here assumed zero) 

°i> a \ = variances of x ± and x 2 
The two variances are assumed equal. The power correlation coefficient is p 2 . A 
portion of Schwartz's results is shown in Fig. 2.25 for several values of the signal 
voltage correlation coefficient. The false-alarm probability is 10 -10 . The results for 



Sec. 2.8] 



The Radar Equation 55 



partial correlation fall between the two extremes of p = (completely uncorrelated) 
and p = 1 (completely correlated), as might have been expected. Also shown is the 
detection probability for a nonfluctuating target signal. The greater the degree of 
correlation between the pulses, the greater must be the signal-to-noise ratio required per 
pulse in order to achieve a specified detection probability. For if, by chance, the first 
pulse were below the mean value necessary for detection, the likelihood is large that all 
the succeeding pulses would be below the mean, if the pulses were highly correlated. 
On the other hand, if the correlation between pulses were weak, it would be likely that 
the below-average pulses would be counterbalanced by the above-average pulses and 
the combined signal-to-noise ratio would average to a value suitable for detection. 
According to Schwartz, the false-alarm probability does not significantly affect the 
general conclusions concerning the partially correlated pulses, at least over the range 
from 10~ 5 to 10~ 10 , the range for which computations were made. The data in Fig. 
2.25 apply to the case of only two pulses. 
When the return echo consists of a train of more 
than two pulses, it is expected that similar con- 
clusions will apply. 

A more general treatment of fluctuating 
pulsed signals in the presence of noise has been 
given by Swerling. 36 His analysis applies to a 
large family of probability-density functions of 
the signal fluctuations and for very general 
correlation properties of the signal fluctuations. 
The effects of the antenna beam shape and of 
nonuniform weighting of pulses by the post- 
detection integrator are also taken into account. 

Scan-to-scan Correlation and the Markov 
Process. It has been experimentally observed 
that in some instances there may be correlation 
between the detection of targets from scan to 
scan; that is, if the target were observed on a 
particular scan, the likelihood would be high 
that it would also be observed on the next scan, 
or if the target is not seen on a particular scan, 
itwould probably not be seen on the next scan. 
The scan-to-scan correlation might be due to 
the slow variations of target aspect or to the 
lobe structure of the antenna pattern. It might 
also be due to atmospheric effects, especially 
when the radar beam just grazes the surface 
of the earth. The above are essentially speculations as to the cause of scan-to-scan 
correlations, for no conclusive experimental proof has been offered to substantiate 
that these are indeed the causes. 

Sponsler 37 has applied the theory of Markov chains to describe the observed scan-to- 
scan correlation. In the theory of Markov chains, the outcome of any particular event 
is not assumed to be independent of other events. Instead, the outcome of any 
particular event is dependent on the outcome of the directly preceding event but not on 
any of the other preceding events. The theory of Markov chains is discussed in texts 
on probability theory. 38 Sponsler presents in his paper some experimental data 
relating the blip-scan ratio T with the transition probability p liX for a particular aircraft 
at a particular range and altitude. The data are attributed to P. S. Olmstead of the 
Bell Telephone Laboratories and are shown in Fig. 2.26. The ordinate is the transition 




0.2 0.4 0.6 0.8 
V, blip-scan ratio 



1.0 



Fig. 2.26. Effect of scan-to-scan correlation 
on detection probability. Experimental 
measurements compared with theory. Solid 
lines are theoretical curves based on scan- 
to-scan correlation with correlation co- 
efficient p (p = corresponds to complete 
independence scan to scan). Solid circles 
and triangles represent detection following 
detection, and open circles and triangles 
represent miss following miss. Circles are 
for outgoing trajectories ; triangles, incoming 
trajectories. (After Sponsler, , 3 ' courtesy IRE 
Trans.) 



56 Introduction to Radar Systems [Sec. 2.9 

probability /Vi, defined as the probability that if a target is detected on a particular scan, 
it will be detected on the next scan. The abscissa is the blip-scan ratio, or the probability 
of detection upon a single scan, with no knowledge assumed as to the previous scans. 
The blip-scan ratio may also be considered as the ratio of the number of times that a 
particular target is observed (as a "blip" on the scope) at a particular range to the 
number of times it could have been observed (scans). Also shown in Fig. 2.26 are the 
theoretical curves that would have been obtained if the data followed a simple Markov 
process. The curves are labeled with the values of the correlation coefficient p between 
successive pairs of observations. The figure seems to indicate that for this particular 
set of data the scan-to-scan correlation coefficient was appro ximately J, if the application 
of the theory of Markov is valid. 

The theory of Markov chains has also been applied by Sponsler 37 to the cumulative 
detection probability of a radar in which the detection decision is made automatically. 

2.9. Transmitter Power 

The power P t in the radar equation (2.1) is called by the radar engineer the peak 
power. The peak pulse power as used in the radar equation is not the instantaneous 
peak power of a sine wave. It is defined as the power averaged over that carrier- 
frequency cycle which occurs at the maximum of the pulse of power. (Peak power is 
usually equal to one-half the maximum instantaneous power.) The average radar 
power P av is also of interest in radar and is defined as the average transmitted power over 
the pulse-repetition period. If the transmitted waveform is a train of rectangular 
pulses of width t and pulse-repetition period T r ( T r = 1 // r ), the average power is related 
to the peak power by 

P av = ^ = p tT f r (2.42) 

The ratio P Av lP t , r/T r , or rf T is called the duty cycle of the radar. A typical pulse radar 
for detection of aircraft might have a duty cycle of 0.001 or less, while a CW radar which 
transmits continuously has a duty cycle of unity. 

Writing the radar equation in terms of the average power rather than the peak power, 
we get 

Ri = P. v GA e on Ei (n) 

(4nfkT F n (B n r)(SIN)J r 

The bandwidth and the pulse width are grouped together since the product of the two is 
usually of the order of unity in most pulse-radar applications. 

If the transmitted waveform is not a rectangular pulse, it is sometimes more conven- 
ient to express the radar equation in terms of the energy E r = P &w jf r contained in the 
transmitted waveform : 

D 4 E T GA e onEi(n) 



(47rfkT F n (B n r)(SIN) 1 



(2.436) 



In this form, the range does not depend explicitly on either the wavelength or the pulse 
repetition frequency. The important parameters affecting range are the total trans- 
mitted energy nE T , the transmitting gain G, the effective receiving aperture A e , and the 
receiver noise figure F n . The type of waveform transmitted and the receiver design 
determine B n r and, to some extent, the integration efficiency E,{n). The signal-to- 
noise ratio {SjN) x depends on the desired probabilities of detection and false' "alarm. 
The target cross section a is not under the control of the radar designer. If a constant 
value of cross section is used, Eq. (2.43) gives the range at which a target of cross section 
a would be detected with a probability P d without exceeding a specified false-alarm 



Sec. 2.10] The Radar Equation 57 

probability P tB , or more specifically without exceeding a specified maximum rate of 
false target indications. If the cross section fluctuates, a must be replaced by its 
average cr av , and (S/N^ and E ( (n) modified according to Figs. 2.23 and 2.24, respectively. 

2.10. Pulse Repetition Frequency and Range Ambiguities 

The pulse repetition frequency (prf) is determined primarily by the maximum range 
at which targets are expected. If the prf is made too high, the likelihood of obtaining 
target echoes from the wrong pulse transmission is increased. Echo signals received 
after an interval exceeding the pulse-repetition period are called multiple-time-around 
echoes. They can result in erroneous or confusing range measurements. The nature of 
some multiple-time-around echoes may cause them to be labeled as "ghost," or "angel," 
targets, or even "flying saucers." Consider the three targets labeled A, B, and C in 
Fig. 2.27a. Target A is located within the maximum unambiguous range -R una mb 
[Eq. (1.2)] of the radar, target B is at a distance greater than iJ unam b DUt " ess tnan 
2/? unamb , while target C is greater than 2i? unamb but less than 3J? unamb . The appearance 
of the three targets on an A-scope is sketched in Fig. 2.27b. The multiple-time-around 
echoes on the A-scope cannot be distinguished from proper target echoes actually 
within the maximum unambiguous range. Only the range measured for target A is 
correct; those for B and C are not. 

n » n x £J1_&LJCJ1 

L^ o *J i I 



"unamu i 

t=o t=Vf r t = */f r t = Vf r 

Time (or range) -»■ 



B C A 

A A A_ 

Range -»■ 
(6) 



Range — *■ 
(c) 

Fig. 2.27. Multiple-time-around echoes, (a) Three targets A, B and C, where A is within R unBLmb , 
and B and C are multiple-time-around targets; (b) appearance of the three targets on the A-scope; 
(c) appearance of the three targets on the A-scope with a changing prf. 

One method of distinguishing multiple-time-around echoes from unambiguous 
echoes is to operate with a varying pulse repetition frequency. 39-42 The echo signal 
from an unambiguous range target will appear at the same place on the A-scope on each 
sweep no matter whether the prf is modulated or not. However, echoes from multiple- 
time-around targets will be spread over a finite range as shown in Fig. 2.27c. The prf 
may be changed continuously within prescribed limits, or it may be changed discretely 
among several predetermined values. The number of separate pulse repetition 
frequencies will depend upon the degree of the multiple-time targets. Second-time 
targets need only two separate repetition frequencies in order to be resolved. 

Instead of modulating the prf, other schemes that might be employed to "mark" 
successive pulses so as to identify multiple-time-around echoes include changing the 
pulse amplitude, pulse width, frequency, phase, or polarization of transmission from 
pulse to pulse. Generally, such schemes are not so successful in practice as one 



58 Introduction to Radar Systems [Sec. 2.11 

would like. One of the fundamental limitations is the foldover of nearby targets ; 
that is, nearby strong ground targets (clutter) can be quite large and can mask weak 
multiple-time-around targets appearing at the same place on the display. Also, more 
time is required to process the data when resolving ambiguities. These techniques to 
resolve ambiguities are similar, in principle, to adding one or more radars and operat- 
ing them on a time-shared basis. 

Ambiguities may theoretically be resolved by observing the variation of the echo 
signal with time (range). Because of the inverse-fourth-power relationship in the 
radar equation, the rate of change of the echo signal from a target at long range will be 
different from that of a target at short range. This is not always a practical technique, 
however, since the echo-signal amplitude can fluctuate strongly for reasons other than a 
change in range. 

An example of the use of high-repetition-rate, ambiguous-range radars is the pulse- 
doppler radar (Sec. 4.5). Range information is usually sacrificed in pulse-doppler- 
radar applications. When used as an AI radar, the number of targets it must handle is 
small ; hence sufficient time is generally available to resolve any ambiguities that might 
exist. But for the general search-radar application, operation with an ambiguous range 
is usually not warranted unless special circumstances make it necessary. A rather 
unique application involving the resolution of range ambiguity is that of the first radar 
detection of Venus (Sec. 14.3). The Millstone Hill radar operated at a prf of 30 cps, 
giving an unambiguous range of about 2,700 nautical miles, but by modulating the 
pulse transmissions it was possible to correctly resolve the ambiguities and measure a 
range almost 9,000 times the unambiguous range of the basic pulse rate. 

2.11. Antenna Parameters 

Almost all radars use directive antennas for transmission and reception. On trans- 
mission, the directive antenna channels the radiated energy into a beam to enhance the 
energy concentrated in the directon of the target. The antenna gain G is a measure of 
the power radiated in a particular direction by a directive antenna to the power which 
would have been radiated in the same direction by an omnidirectional antenna with 
100 per cent efficiency. More precisely, the power gain of an antenna used for trans- 
mission is 

/-vfl m\ Power radiated per unit solid angle in azimuth 6 and elevation <j> 

G(p,<f>) = s- — -2 r (2.44) 

power delivered to antenna/47r 

Note that the antenna gain is a function of direction. If it is greater than unity in some 
directions, it must be less than unity in other directions. This follows from the con- 
servation of energy. When we speak of antenna gain in relation to the radar equation, 
we shall usually mean the maximum gain G, unless otherwise specified. One of the 
basic principles of antenna theory is that of reciprocity, which states that the properties 
of an antenna are the same no matter whether it is used for transmission or reception. 
Hence the gain and the effective area of a transmitting antenna are the same when the 
antenna is used for receiving. It will be recalled that this principle was used in the 
derivation of the radar equation in Sec. 1 .2. 

The antenna beam pattern, or simply the antenna pattern, is a plot of antenna gain as 
a function of the direction of radiation. (A typical antenna pattern plotted as a function 
of one angular coordinate is shown in Fig. 7. 1 .) Antenna beam shapes most commonly 
employed in radar are the pencil beam (Fig. 2.28a) and the fan beam (Fig. 2.28Z>). The 
pencil beam is axially symmetric, or nearly so. Beamwidths of typical pencil-beam 
antennas may be of the order of a few degrees or less. Pencil beams are commonly used 
where it is necessary to measure continuously the angular position of a single target in 
both azimuth and elevation, as, for example, the target-tracking radar for the control of 



Sec. 2.11] 



The Radar Equation 59 



weapons or missile guidance. The pencil beam may be generated with a metallic 
reflector surface shaped in the form of a paraboloid of revolution with the electro- 
magnetic energy fed from a point source placed at the focus. 

Although a narrow beam can, if necessary, search a large sector or even a hemisphere, 
it is not always desirable to do so. Usually, operational requirements place a restriction 
on the maximum scan time (time for the beam to return to the same point in space) so 
that the radar cannot dwell too long at any one radar resolution cell.| This is especially 
true if there is a large number of resolution cells to be searched. The number of 
resolution cells can be materially reduced if the narrow angular resolution cell of a 
pencil-beam radar is replaced by a beam in which one dimension is broad while the 
other dimension is narrow, that is, a fan-shaped pattern. One method of generating a 
fan beam is with a parabolic reflector shaped to yield the proper ratio between the 
azimuth and elevation beamwidths (Fig. 1.6). Many long-range ground-based search 
radars use a fan-beam pattern narrow in 
azimuth and broad in elevation 

When ground-based search radars em- 
ploying fan beams are used against air- 
craft targets, no resolution in elevation 
is obtained. Therefore no height infor- 
mation is available. One method of 
achieving elevation-angle information for 
targets located by a fan-beam search radar 
is to employ an additional fan-beam radar 
with the narrow dimension in elevation 
instead of in azimuth, as in the common 
height-finding radar. (Strictly speaking, 
a height-finding radar actually measures 
elevation angle rather than height.) 

If a fan-beam search radar 1 ° in azimuth 
and 45° in elevation were required to scan 
360° in azimuth (complete circular cover- 
age), the scanning region might be con- 
sidered as being divided into 360 angular 
resolution cells. On the other hand, if a 
pencil-beam radar with a beamwidth of 
1° were required to scan the samevolume, 
the total number of angular resolution 

cells would be 360 x 45 = 16,200. Since the number of resolution cells which the 
fan-beam radar must search is considerably less than the number which the pencil- 
beam radar must search, the fan-beam radar can dwell longer in eachcell and more hits 
per target can be obtained. 

The rate at which a fan-beam antenna may be scanned is a compromise between the 
rate at which target-position information is desired (data rate) and the ability to detect 
weak targets (probability of detection). Unfortunately, the two are at odds with one 
another. The more slowly the radar antenna scans, the more pulses will be available 
for integration and the better the detection capability. On the other hand, a slow scan 
rate means a longer time between looks at the target. Scan rates of practical search 
radars vary from 1 to 60 rpm, 5 or 6 rpm being typical. 

The coverage of a simple fan beam is usually inadequate for targets at high altitudes 
close to the radar. The simple fan-beam antenna radiates very little of its energy in 

t The radar resolution cell is in general a five-dimensional space (two orthogonal-angle coordinates, 
range, doppler velocity, and time). 




Fig. 2.28. (a) Pencil-beam-antenna pattern; 
(6) fan-beam-antenna pattern. 



K,~^ (2.46) 



60 Introduction to Radar Systems [Sec. 2.11 

this direction. However, it is possible to modify the antenna pattern to radiate more 
energy at higher angles. One technique for accomplishing this is to employ a fan beam 
with a shape proportional to the square of the cosecant of the elevation angle. In the 
cosecant-squared antenna (Sec. 7.9), the gain as a function of elevation angle is given by 

G(<£) = G(<£ )-^i for <f> <<fx<f> m (2.45) 

csC <p 

where G(<£) = gain at elevation angle <f> 

<A)> ^m = angular limits between which beam follows esc 2 shape 
This applies to the airborne search radar observing ground targets as well as ground- 
based radars observing aircraft targets. In the airborne case, the angle ^ is the 
depression angle. From <f> = to <f> = (f> , the antenna pattern is similar to a 
normal antenna pattern, but from <f> = </>„ to <f> = <f> m , the antenna gain varies as esc 2 <f>. 
Ideally, the upper limit <f> m should be 90°, but it is always much less than this with a 
single antenna because of practical difficulties. The cosecant-squared antenna may be 
generated by a distorted section of a parabola or by a true parabola with a properly 
designed set of multiple feed horns. The cosecant-squared pattern may also be 
generated with an array-type antenna. 

The cosecant-squared antenna has the important property that the echo power P r 
received from a target of constant cross section at constant altitude h is independent of 
the target's range R from the radar. Substituting the gain of the cosecant-squared 
antenna [Eq. (2.45)] into the simple radar equation (1.106) gives 

p = P k G\<j> ) esc 4 <f>X 2 o = K cscV 
(47r) 3 csc 4 </. i? 4 1 J? 4 

where K x is a constant. The height h of the target is assumed constant, and since 
esc <j> = Rjh, the received power becomes 

p r = KJ* = K 2 (2.47) 

where K 2 is a constant. The echo signal is therefore independent of range for a con- 
stant-altitude target. 

In practice, the power received from an antenna with a cosecant-squared pattern is 
not truly independent of range because of the simplifying assumptions made. The 
cross section a varies with the viewing aspect, the earth is not flat, and the radiation 
pattern of any real antenna can be made to only approximate the desired cosecant- 
squared pattern. The gain of a typical cosecant-squared antenna used for ground- 
based search radar might be about 2 db less than if a fan beam were generated by the 
same aperture. 

The maximum gain of an antenna is related to its physical area A (aperture) by 

G = 4 -f- P (2.48) 

where p = antenna efficiency 

X = wavelength of radiated energy 
The antenna efficiency depends on the aperture illumination and the efficiency of the 
antenna feed. The product of pA is the effective aperture A e . A typical reflector 
antenna with a parabolic shape will produce a beamwidth approximately equal to 

6° = — ' (2.49) 

where / is the dimension of the antenna in the plane of the angle 6, and X and / are 
measured in the same units. The value of the constant, in this case taken to be 65, 
depends upon the distribution of energy (illumination) across the aperture. 



Sec. 2.12] 



The Radar Equation 61 



2.12. System Losses 

At the beginning of this chapter it was mentioned that one of the important factors 
omitted from the simple radar equation was the losses that occur throughout the radar 
system. The losses reduce the signal-to-noise ratio at the receiver output. They may 
be of two kinds, depending upon whether or not they can be predicted with any degree 
of precision beforehand. The antenna beam-shape loss, collapsing loss, and losses in 
the microwave plumbing are examples of losses which can be calculated if the system 
configuration is known. These losses are very real and cannot be ignored in any 
serious prediction of radar performance. The loss due to the integration of many 
pulses (or integration efficiency) has already been mentioned in Sec. 2.6 and need not be 



10 



1.0 



o 
o 



i — n i ii 1 1 1 : — i i i i iii| 



TTI 



^0.90 xO.40 
\ 1.122 x 0.497 
\l.372 x 0.622 

\ 1.872 x 0.872 



x 2.84 X1.34 
^ 3.4x1.7 , 

4.3x2.15 <£ 




0.01 



I l l l I ll I I I I I I 111 1 1 I I I I II 



0.1 



1.0 10 

Frequency, qigocycles 



100 



Fig 2 29. Theoretical (one-way) attenuation of RF transmission lines. Waveguide sizes are in inches 
and are the inside dimensions. (Data from Armed Services Index of R.F. Transmission Lines and 
Fittings, ASESA, 49-2B.) 

discussed further. Losses not readily subject to calculation and which are less predict- 
able include those due to field degradation and to operator fatigue or lack of operator 
motivation. Estimates of the latter type of loss must be made on the basis of prior 
experience and experimental observations. They may be subject to considerable 
variation and uncertainty. Although the loss associated with any one factor may be 
small, there are many possible loss mechanisms in a complete radar system, and their 
sum total can be significant. 

In this section, loss (number greater than unity) and efficiency (number less than 
unity) are used interchangeably. One is simply the reciprocal of the other. 

Plumbing Loss. There is always some finite loss experienced in the transmission 
lines which connect the output of the transmitter to the antenna. The losses in decibels 
per 100 ft for radar transmission lines are shown in Fig. 2.29. At the lower radar 
frequencies the transmission line introduces little loss, unless its length is exceptionally 
long. At the higher radar frequencies, attenuation may not always be small and may 
have to be taken into account. In addition to the losses in the transmission line itself, 



62 Introduction to Radar Systems [Sec. 2.12 

an additional loss can occur at each connection or bend in the line and at the rotary 
antenna joint if used. Connector losses are usually small, but if the connection is 
poorly made, it can contribute significant attenuation. Since the same transmission 
line is generally used for both receiving and transmission, the loss to be inserted in the 
radar equation is twice the one-way loss. 

The received signal suffers some attenuation as it passes through the unfired TR tube 
on its way to the receiver. Generally, the greater the isolation required from the 
duplexer on transmission, the larger will be the insertion loss on reception. By 
insertion loss is meant the loss introduced when the component, in this case the duplexer, 
is inserted into the transmission line. The precise value of the insertion loss depends to 
a large extent on the particular design. For a typical duplexer it might be of the order 
of 1 db (Sec. 8.11). The duplexer also introduces loss when in the fired condition (arc 
loss) ; approximately 1 db is typical. 

In an 5-band (3,000 Mc) radar, for example, the plumbing losses might be as follows : 

100 ft of RG-l 13/U Al waveguide transmission line (two-way) 1 .0 db 

Loss due to poor connections (estimate) 0.5 db 

Rotary-joint loss 0.4 db 

Duplexer loss 1.5 db 

Total plumbing loss 3.4 db 

Beam-shape Loss. The antenna gain that appears in the radar equation was assumed 
to be a constant equal to the maximum value. But in reality it is unlikely that the 
target will always be in the direction corresponding to maximum gain. If the antenna 
scans past the target, the amplitude of the returned pulses will be modulated by the 
beam shape. Therefore it is incorrect to assume a constant value of gain equal to the 
maximum for each pulse, unless the antenna pattern is rectangular in shape. Antenna 
beams are not rectangular ; hence the amplitudes of the echo pulses will vary as the shape 
of the antenna pattern. The total energy from a group of echo pulses radiated and 
collected by a practical antenna will be less than that which would have been received 
from an antenna with a rectangular pattern whose gain was equal to the maximum gain 
of the practical antenna. The loss in received energy may be taken into account by 
employing an average value of the antenna gain, or alternatively, the maximum 
antenna gain may be substituted into the radar equation and a beam-shape loss 
introduced. The two methods are equivalent. The latter is normally used. 

The one-way-power (two-way- voltage) antenna pattern may be approximated by the 
Gaussian expression exp (— a 2 d 2 ), where 6 is the angle measured from the center of the 
beam, a 2 is a constant equal to 2.776/6%, and 6 B is the beamwidth measured between 
half-power points. This expression for the antenna pattern is valid in the vicinity of 
the center of the beam. It deviates considerably from the actual antenna pattern at 
angles too far from the center of the beam, because the Gaussian function does not 
represent the sidelobe radiation of the normal antenna. 

Consider the train of radar pulses to be so oriented relative to the antenna pattern 
that one of the pulses is coincident with the beam center. This assumption is made for 
convenience, but similar results can be obtained with any other arbitrary time relation- 
ship between the train of radar pulses and the beam center. It is further assumed that 
a transmitted pulse and its received echo occur at essentially the same point of the 
antenna pattern. The echo signal power received by the radar when the pulse is 
transmitted and received from the beam center is denoted as S v The total signal power 
represented by n pulses received with the Gaussian antenna pattern and integrated 
without further loss is 

? [~i , </" v /2 -5.55fe 2 ( A0) 2 l 

S 1 1 + 2 _2 exp — i — '- (2.50) 



U B 



Sec. 2.12] The Radar Equation 63 

where A0 is the angular separation between pulses. The beam-shape loss (number 
greater than unity) relative to a radar that integrates all n pulses with an antenna gain 
corresponding to that at beam center is 

ft 

Beam-shape loss = (n _ 1)/2 (2-51) 

1+2 2 exp [-5.55fe 2 (A0) 2 /^] 



k = l 



This may be put in another form by noting that A0 = 6 B /n B , where n B is the number of 
pulses received between the 3-db beamwidth. Making this substitution, we have 

Beam-shape loss = { n -i)n (2-52) 

1 + 2^2 exp(-5.55k 2 /n|) 

For example, if we integrate 1 1 pulses, all lying uniformly between the 3-db beamwidth, 
the loss is 1.96 db. 

The beam-shape loss considered above was for a beam shaped in one plane only. It 
applies to a fan beam, or to a pencil beam if the target passes through its center. If the 
target passes through any other point of the pencil beam, the maximum signal received 
will not correspond to the signal from the beam center. The beam-shape loss is 
reduced by the ratio of the square of the maximum antenna gain at which the pulses 
were transmitted divided by the square of the antenna gain at beam center. The ratio 
involves the square because of the two-way transit. If the target passes at the outer 
edge of the antenna 3-db beamwidth, the beam-shape loss would be increased by 
approximately 6 db over that given by Eq. (2.52). 

The antenna scanning speed was assumed slow enough so that the gain on trans- 
mission is the same as the gain on reception. If this were not so, an additional loss, 
called the scanning loss, would have to be computed. The techniques for computing 
scanning loss are similar in principle to those for computing beam-shape loss. Scan- 
ning loss is important for rapid-scan antennas or for very long range radars such as those 
designed to view extraterrestrial objects. 

If the antenna is stationary (searchlighting the target), the transmitted pulses and 
echo pulses all appear at the same place in the antenna beam. The beam-shape loss in 
this case is simply 



Beam-shape loss = exp 



e 2 e 2 \ 

5 55 Zsl _i_ ils. 

xo Ba °Be' 



(2.53) 



where d a = azimuth angle between target and antenna 
6 Ba = azimuth half-power beamwidth 

6 e = elevation angle between target and antenna 
Q Be = elevation half-power beamwidth 

Limiting Loss. If the signal is limited in the receiver, the probability of detection 
will be lowered, everything else being held constant. Although a well-designed and 
engineered receiver will not limit the received signal under normal circumstances, 
intensity-modulated CRT displays such as the PPI and the B-scope have limited 
dynamic range and may limit. According to Marcum, 10 limiting results in a loss of 
only a fraction of a decibel for a large number of pulses integrated, provided the limiting 
ratio (ratio of video limit level to rms noise level) is as large as 2 or 3. 

Other analyses of bandpass limiters show that for small signal-to-noise ratios, the 
reduction in the signal-to-noise ratio of a sine- wave signal imbedded in narrowband 
Gaussian noise is tt/4 (about 1 db). 43 However, by appropriately shaping the spectrum 
of the input noise, the degradation can be made negligibly small. 44 Results derived 



64 Introduction to Radar Systems [Sec. 2.12 

from an analysis of signal-to-noise ratios alone, however, are not necessarily related to 
signal detectability with an operator or an electronic threshold detector. A realistic 
analysis of detectability should be based on the statistics of signal and noise and include 
the probabilities of detection and false alarm. 

Collapsing Loss. It may happen that the radar integrates a number of unwanted 
noise samples along with the wanted signal-plus-noise pulses. The noise added to the 
signal results in a degradation of the signal-to-noise ratio, accounted for by the collapsing 
loss. Collapsing loss occurs in cathode-ray-tube displays which collapse range 
information, such as the C-scope (plot of elevation angle vs. azimuth angle). The echo 
signal from a particular range interval must compete in a collapsed-range display, not 
only with the noise energy contained within that range interval, but with the noise 
energy from all other range intervals at the same elevation and azimuth. Another 
example of collapsing loss occurs if the video bandwidth is smaller than optimum since 
the effect is the same as integrating additional noise samples (unless range gating is 
used). 

A collapsing loss also results if the output of two or more radar receivers is combined 
and only one of the receivers contains signal while the other contains noise, as, for 
example, in video mixing (where more than one radar output is superimposed on the 
same indicator) or polarization diversity. The collapsing loss may be defined as 

where {SjN) m+n is the signal-to-noise ratio per pulse required for detection when there 
are m extra noise pulses integrated along with n signal-plus-noise pulses, and (S/N)„ is 
the signal-to-noise ratio per pulse required when no extra noise pulses are present. 

The mathematical derivation of the collapsing loss may be carried out as suggested 
by Marcum, 10 who has shown that the integration of m noise pulses, along with n 
signal-plus-noise pulses with signal-to-noise ratio per pulse (S/N), is equivalent to the 
integration of m + n signal-plus-noise pulses each with signal-to-noise ratio {SjN)lR c . 
The collapsing ratio R c is defined as 

R< = ^^ (2.55) 

n 

where m = number of extra noise pulses 

n = number of signal-plus-noise pulses 

Mathematically, the collapsing loss is equivalent to the integration of m + n signal 

pulses instead of «. 10 The collapsing loss is thus equal to the ratio of the integration 

loss L, for m + n pulses to the integration loss for n pulses, or 

L c{m ,n) = M^O (Z56a) 

In terms of the integration-improvement factor I t {n), the collapsing loss is 

L c (m,n) = R ^ n \ {2 .56b) 

Ii(m + n) 

For example, assume that 10 signal-plus-noise pulses are integrated along with 30 
noise pulses and the P a = 0.90 and n t = 10 8 . From Fig. 2.8fc, L,(40) is 3.5 db and 
L/10) is 1.7 db, so that the collapsing loss is 1.8 db. 

Nonideal Equipment. The transmitter power introduced into the radar equation 
was assumed to be the output power (either peak or average). However, transmitting 
tubes are not all uniform in quality, nor should it be expected that any individual tube 



Sec. 2.12] The Radar Equation 65 

will remain at the same level of performance throughout its useful life. Thus, for 
one reason or another, the transmitted power may be less than the design value. To 
account for this, the value of the transmitted power inserted into the radar equation 
should be less than the advertised, or design, power. The reduction in power varies, 
of course, with the application and the type of tube, but lacking a better number, a 
reduction of the order of 2 db might be used as an approximate value for system design 
purposes. 

Only a receiver "matched" in the communication-theory sense makes optimum use 
of the total signal energy contained in the target echo signal. A matched receiver may 
be only approximated in practice; thus an additional loss must be introduced into the 
radar system. The amount of loss expected with various types of nonmatched re- 
ceivers is shown in Table 9.1. A typical value of loss for a nonmatched receiver might 
be about 1 db. Variations in receiver noise figure are also to be expected. 

It will be recalled that the usual detection criterion indicates the presence of a target 
whenever the envelope of the signal crosses a threshold. Because of the exponential 
relationship between the false-alarm time and the threshold level [Eq. (2.26)], a slight 
change in the threshold level can cause a significant change in the false-alarm time. In 
practice, therefore, it may be necessary to set the threshold level slightly higher than 
calculated, so that, in the event of circuit instabilities— and these need only be slight — 
the false-alarm time will not be reduced to an intolerable level. The amount by which 
the receiver threshold should be increased depends upon the application and the 
stability of the circuits. 

Operator Loss. An operator's capacity for searching a CRT display and recognizing 
the presence of target echoes is limited. The information bandwidth of a human radar 
operator is of the order of 10 cps (20 bits/sec). If the operator is fatigued or not 
sufficiently motivated, the information bandwidth that can be adequately handled may 
be even less. The rate at which information can be displayed on a PPI is many times 
the capacity of the operator bandwidth. If, for example, the radar display contained 
180 resolvable elements in azimuth and 20 elements in range, the total number of 
resolution cells on one revolution of the antenna would be 3,600. If the time for one 
revolution were 12 sec, data could appear on the PPI at a rate of 300 bits/sec. By the 
Shannon sampling theorem, this corresponds to a minimum bandwidth of 150 cps, 
which is far beyond the operator's ability to handle. This mismatch in bandwidth can 
result in a loss in operator performance. Another factor contributing to operator loss 
occurs when he resorts to guessing, as when he becomes overloaded or panicky. 

Based on both empirical and experimental results, an operator-efficiency factor is 
approximately given by the following expression: 

Po = 0.7y> 2 (2.57) 

where y> is the single-scan probability of detection (blip-scan ratio). 45 This assumes a 
good operator observing a PPI presentation under good conditions. Under less 
favorable conditions, the operator efficiency might be somewhat less. The operator 
factor is not linear with detection probability y>. Even with y> = 1, the efficiency is 
only 0.7, corresponding to a 1.5-db loss in signal-to-noise ratio. When the single- 
scan detection probability is 0.5, the operator efficiency is 0.175, or a loss of about 

7.5 db. 

Much higher losses than a few decibels have sometimes been attributed to the oper- 
ator. However, it seems that in a large number of reported cases, other loss mecha- 
nisms besides the operator were included in the operator loss. Two loss mechanisms 
sometimes blamed on the operator are unaccounted-for propagation effects and the 
losses due to field degradation. It would seem better, whenever possible, to consider 
these losses separately. 



66 Introduction to Radar Systems [Sec. 2.13 

Field Degradation. When a radar system is operated under laboratory conditions 
by engineering personnel and experienced technicians, the inclusion of the above losses 
into the radar equation should give a realistic description of the performance of the 
radar under normal conditions (ignoring anomalous propagation effects). However, 
when a radar is operated under field conditions, the performance usually deteriorates 
even more than can be accounted for by the above losses, especially when the equipment 
is operated and maintained by inexperienced or unmotivated personnel. It may even 
apply, to some extent, to equipment operated by professional engineers under adverse 
field conditions. Factors which contribute to field degradation are poor tuning, weak 
tubes, water in the transmission lines, incorrect mixer-crystal current, deterioration of 
receiver noise figure, poor TR tube recovery, loose cable connections, etc. 

To minimize field degradation, radars should be designed with built-in automatic 
performance-monitoring equipment. Careful observation of performance-monitoring 
instruments and timely preventative maintenance can do much to keep radar perform- 
ance up to design level. Radar characteristics that might be monitored include 
transmitter power, receiver noise figure, the spectrum and/or shape of the transmitted 
pulse, and the decay time of the TR tube. 

A good estimate of the field degradation is difficult to obtain since it cannot be 
predicted and is dependent upon the particular radar design and the conditions under 
which it is operating. A degradation of 3 db is sometimes assumed when no other 
information is available. 

Other Loss Factors. A radar designed to discriminate between moving targets and 
stationary objects (MTI radar) may introduce additional loss over a radar without this 
facility. The MTI discrimination technique results in complete loss of sensitivity for 
certain values of target velocity relative to the radar. These are called blind speeds. 
The blind-speed problem and the loss resulting therefrom are discussed in more detail 
in Chap. 4. 

In a radar with overlapping range gates, the gates may be wider than optimum for 
practical reasons. The additional noise introduced by the nonoptimum gate width 
will result in some degradation. 

Another factor that has a profound effect on the radar range performance is the 
propagation medium discussed briefly in the next section and in Chap. 11. 

There are many causes of loss and inefficiency in a radar. Although they may each 
be small, the sum total can result in a significant reduction in radar performance. It is 
important to understand the origins of these losses, not only for better predictions of 
radar range, but also for the purpose of keeping them to a minimum by careful radar 
design. 

2.13. Propagation Effects 

In analyzing radar performance it is convenient to assume that the radar and target 
are both located in free space. However, there are very few radar applications which 
approximate free-space conditions. One of the few cases which might is a target at 
high altitude close to the radar with the surface of the earth nonreflecting at the frequency 
of radar operation. In most cases of practical interest, the earth's surface and the 
medium in which radar waves propagate can have a significant effect on radar perform- 
ance. In some instances the propagation factors might be important enough to 
overshadow all other factors that contribute to abnormal radar performance. The 
effects of non-free-space propagation on the radar are of three categories : (1) attenuation 
of the radar wave as it propagates through the earth's atmosphere, (2) refraction of the 
radar wave by the earth's atmosphere, and (3) lobe structure caused by interference 
between the direct wave from radar to target and the wave which arrives at the target via 
reflection from the ground. 



Sec. 2.14] The Radar Equation 67 

Attenuation. The gases and water vapor constituting the earth's atmosphere 
attenuate electromagnetic radiation. The result is a loss of intensity over that experi- 
enced if in free space. The amount of attenuation depends upon the frequency of 
operation as well as the gas constituting the medium. Atmospheric attenuation is 
essentially negligible at the lower end of the radar frequency spectrum, but it may be 
quite important at frequencies above X band. In fact, the relatively large attenuation 
of millimeter- wavelength radiation is one of the factors which determine the upper limit 
of usable radar frequencies. 

The two-way attenuation of the radar signal in the atmosphere is exp (2a/?), where a 
is the attenuation constant and R is the range. Typical values of the attenuation 
constant are given in Sec. 11.8. The attenuation factor exp (2ajR) must be included in 
the radar equation if a is large or if the propagation path is long. When this factor is 
included, the solution of the radar equation for range is not simple, because of the 
exponential relationship. An approximate method of accounting for attenuation is to 
solve for the range as if attenuation were absent and reduce the range found in this 
manner according to the amount of attenuation. 

In addition to attenuation by atmospheric gases, the radar signal will suffer con- 
siderable attenuation near the region of the geometrical line of sight and beyond (Sec. 
11.6). The attenuation of electromagnetic waves in the diffraction region beyond the 
line of sight is so severe that, for all practical purposes, normal radars may be said to be 
limited to line-of-sight propagation or less. 

Refraction. The density of the atmosphere is not uniform with altitude. The 
gradient of density results in a bending of the radar waves in a manner analogous to the 
bending of light waves by an optical prism. Water vapor is the atmospheric compo- 
nent chiefly responsible for the bending of radar waves in the lower atmosphere. The 
atmosphere is usually denser at the lower altitudes; consequently radar waves will 
normally be bent around the earth. Therefore the radar, if powerful enough, can see 
around the curvature of the earth beyond the limits of the geometrical line of sight. In 
some cases, conditions may be quite favorable and large amounts of bending will be 
experienced, with the result that the radar range will be considerably increased. This 
condition is called superrefraction, or ducting, and is a form of anomalous propagation. 
The density gradient of the water vapor can also be such that the radar wave is bent 
upward, and the radar range will be less than it would normally be. These abnormal 
effects on radar could be predicted if sufficient meteorological data were available. 
However, the process of obtaining the proper type of data is expensive and probably 
cannot be considered as standard radar practice except under special circumstances. 
This is unfortunate, since the effects of anomalous propagation conditions can be quite 
pronounced and may be the largest single factor contributing to inaccurate radar 
predictions. 

Lobing. The presence of the earth's surface not only restricts the line of sight, but 
it can also have a serious effect on the radar coverage for targets within the line of sight. 
Two waves arrive at the target via two separate paths . One arrives over the direct path 
from radar to target; the other path includes a reflection from the ground. The two 
waves can interfere destructively or constructively, depending on their relative phase, 
and the echo signal may be larger than if in free space or it may be smaller. In Sec. 1 1 .2 
it is shown that the radar range theoretically can be increased at certain elevation angles 
by as much as a factor of 2 over the free-space range, at the expense of zero coverage at 
other angles. 

2.14. Summary 

Prediction of Radar Range. In this chapter, some of the more important factors that 
enter into the radar equation for the prediction of range were briefly considered . The 



68 Introduction to Radar Systems [Sec. 2.14 

radar equation (2.1), with the modifications indicated in this chapter, becomes 
o4 PnvGApanEjin) exp (2aK ma x) 

"max = — — — (2.58) 

where i? max = maximum radar range, m 
G = antenna gain 
A = antenna aperture, m 2 
p = antenna efficiency 
n = number of hits integrated 
£■<(«) = integration efficiency (less than unity) 

L s = system losses (greater than unity) not included in other parameters 
a = attenuation constant of propagation medium 
a = radar cross section of target, m 2 
F n = noise figure 

k = Boltzmann's constant = 1.38 x 10" 23 joule/deg 
T = standard temperature = 290°K 
B n = receiver noise bandwidth, cps 
t = pulse width, sec 
f r = pulse repetition frequency, cps 
(S/N)i = signal-to-noise ratio required at receiver output (based on single-hit 
detection) 
In some applications it is more appropriate to replace P av /f r = P k r by E„ the energy 
transmitted per pulse. 
Other auxiliary relations useful when dealing with the radar equation are 

" ~° Bfr (2.30) 

(2.48) 
duty cycle (2.59) 



"2? 


6ft> m 


G 


AirAp 
X 2 


Jav 
~P~t 


= Tf r = 


P, 


n 



(2.60) 
(2.6: 
(2.49) 



B n Tia. n f 
B n r sa 1 for most radar applications (2.61) 

a 65A 

where n B = number of pulses received within half-power antenna beamwidth 6 B 

co m = antenna rotation rate, rpm 

P t = peak power 

Pfa = probability of false alarm 

r fa = average false-alarm time 
/ = linear antenna dimension 
Figure 2.7 may be used to obtain the value of{SjN\, given the probabilities of detection 
and false alarm. The false-alarm probability follows from the specified average 
false-alarm time [Eq. (2.60)]. If n pulses are integrated postdetection, the integration- 
improvement factor may be obtained from Fig. 2.8a. A fluctuating target cross 
section requires that the average value of a be substituted in the radar equation and that 
the signal-to-noise ratio per pulse and the integration-improvement factor be modified 
according to Figs. 2.23 and 2.24, respectively. The maximum radar range is a statistical 
quantity, depending mainly on the statistics of a, (S/N)^ and the propagation factors. 



The Radar Equation 



69 



Sec. 2.14] 

The radar equation developed in this chapter applies primarily to a pulse radar, although 
it may be readily modified to accommodate CW, FM-CW, pulse-doppler, MTI, or 
tracking radar. 46-48 Equation (2.58) can be generally applied to a CW radar if P av // r is 
replaced by E t (the energy transmitted during the target observation time t) and if the 
integration-improvement factor is made equal to unity. 

The radar range equation is strictly valid in the far zone (Fraunhofer region) of the 
antenna. If the target is in the Fresnel region [R < {D a + D T ) 2 M, where D a = 
antenna diameter, D T = target diameter, and X = wavelength], the antenna gain G 
and effective area normally associated with the far zone decrease. 49 - 50 Generally, the 
Fresnel region is much shorter than practical radar ranges and can usually be ignored. 



0.99 


1 


0.98 


— Cose 


0.95 




1 0.90 


— 


~ 0.80 


- 


o 0.70 


- 


■2 0.60 


- 


° 0.50 
1 0.40 


_ 


.9- 0.30 


- 


0.20 


- 


0.10 
0.05 


i 



0.2 




1.6 



1.8 



2.0 



Fig. 2.30. Examples of theoretical blip-scan curves, n = 10 hits integrated and n, = 10". Case 5 is 
for a nonfluctuating cross section; case 1 represents a cross-section fluctuation described by Rayleigh 
statistics, correlated scan to scan; and case 2 represents a Rayleigh cross-section fluctuation with 
pulse-to-pulse correlation. R M = 1 corresponds to the range at which the blip-scan ratio for a non- 
fluctuating target is 0.50. 

However, with a large antenna at high microwave frequencies the Fresnel region can- 
not always be ignored. For example, a 1 20-ft-diameter antenna operating at 8,000 Mc 
has a value of D 2 /X of about 19 nautical miles. The antenna gain in the Fresnel region 
can be restored by focusing the antenna to the target range. The antenna pattern 
through the focal plane is the same as that at infinity. 

Perhaps the most important factor not explicitly included in Eq. (2.58) is the effect of 
anomalous propagation. It is difficult to properly take account of propagation in 
an exact manner, although reasonable safety factors may be assumed in order to set an 
upper bound on its effects. 

A figure of merit sometimes used to express the relative performance of radar is the 
radar performance figure, defined as the ratio of the pulse power of the radar transmitter 
to the power of the minimum signal detectable by the receiver. 

Further consideration of the radar equation will be given in Chap. 13, where it is 
used as the basis for radar system design. 

Blip-scan Ratio and Detection Probability. A practical method of measuring the 
performance of search radars operating in the field is to fly an aircraft on a radial course 
and record on each scan of the antenna whether or not the target is detected. This is 
repeated many times until sufficient data are obtained to compute the average number 



70 Introduction to Radar Systems [Sec. 2.14 

of scans the target was seen at a particular range (blips) to the total number of times it 
could have been seen (scans). This is called the blip-scan ratio. It is the probability 
per scan for a particular target at a particular range, altitude, and aspect. The aspects 
commonly considered are either head on or from the rear. These are the two easiest to 
provide in actual field experiments. The experimentally found blip-scan ratio curve is 
subject to many limitations, but it attempts to evaluate the performance of an actual 
radar equipment under somewhat controlled and realistic conditions. 

Examples of theoretical blip-scan curves are shown in Fig. 2.30. These were 
computed from Fig. 2.22, assuming that the radar integrates 10 hits and that the false- 
alarm number n f = 10 8 . The three curves represent a nonfluctuating cross section 
(case 5), a cross-section fluctuation described by Rayleigh statistics, correlated scan to 
scan (case 1), and a Rayleigh cross-section fluctuation with pulse-to-pulse correlation 
(case 2). The abscissa is plotted in terms of R m , the range at which the detection 
probability for a nonfluctuating cross section is 0.50. 

The plot of blip-scan ratio as a function of range should not be confused with the 
cumulative detection probability as a function of range. The latter is defined as the 
cumulative probability of detecting a particular target by the time it reaches a particular 
range. It may be computed from the blip-scan data and the scan rate. 



REFERENCES 



1. Ridenour, L. N.: "Radar System Engineering," MIT Radiation Laboratory Series, vol. 1, p 592 
McGraw-Hill Book Company, Inc., New York, 1947. 

2. Wiener, N.: "Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with 
Engineering Applications," John Wiley & Sons, Inc., New York, 1949. 

3. Van Vleck, J. H., and D. Middleton: A Theoretical Comparison of the Visual, Aural, and Meter 
Reception of Pulsed Signals in the Presence of Noise, /. Appl. Phvs .vol 17 dd 940-971 
November, 1946. rr J ' ' FK ' ' 

4. Bennett, W. R. : Methods of Solving Noise Problems, Proc. IRE, vol. 44, pp. 609-638, May, 1956. 

5. Davenport, W. B., and W. L. Root: "Introduction to Random Signals and Noise," McGraw-Hill 
Book Company, Inc., New York, 1958. 

6. Bendat, J. S.: "Principles and Applications of Random Noise Theory," John Wiley & Sons Inc 
New York, 1958. J 

7. Helstrom, C. W.: "Statistical Theory of Signal Detection," Pergamon Press, New York, 1960 

8. Parzen, E.: "Modern Probability Theory and Its Applications," John Wiley & Sons, Inc New 
York, 1960. 

9. Rice, S. O. : Mathematical Analysis of Random Noise, Bell System Tech J vol 23 pp 282-332 
1944, and vol. 24, pp. 46-156, 1945. ' 

10. Marcum, J. I. : A Statistical Theory of Target Detection by Pulsed Radar, Mathematical Appendix 
IRE Trans., vol. IT-6, pp. 145-267, April, 1960. 

11. Hollis, R.: False Alarm Time in Pulse Radar, Proc. IRE, vol. 42, p. 1189, July, 1954. 

12. Harrington, J. V., and T. F. Rogers: Signal-to-noise Improvement through' Integration in a 
Storage Tube, Proc. IRE, vol. 38, pp. 1197-1203, October, 1950. 

13. Mentzer, J. R.: "Scattering and Diffraction of Radio Waves," Pergamon Press, New York, 1955 

14. King, R. W. P., and T. T. Wu: "The Scattering and Diffraction of Waves," Harvard University 
Press, Cambridge, Mass., 1959. 

15. Weil, H., M. L. Barasch, and T. A. Kaplan: Scattering of Electomagnetic Waves by Spheres 
Univ. Michigan Eng. Research Inst. Rept. 2255-20-T, July, 1956. 

16. Siegel, K. M., F. V. Schultz, B. H. Gere, and F. B. Sleator: The Theoretical and Numerical 
Determination of the Radar Cross Section of a Prolate Spheroid, IRE Trans vol AP-4 nn 
266-275, July, 1956. " VV ' 

17. Mathur, P. N., and E. A. Mueller: Radar Back-scattering Cross Sections for Nonspherical 
Targets, IRE Trans., vol. AP-4, pp. 51-53, January, 1956. 

18. Scharfman, H.: Scattering from Dielectric Coated Spheres in the Region of the First Resonance 
J. Appl. Phys., vol. 25, pp. 1352-1356, November, 1954. 

19. Andreasen, M. G. : Back-scattering Cross Section of a Thin, Dielectric, Spherical Shell, IRE Trans 
vol. AP-5, pp. 267-270, July, 1957. 

20. King, D. D.: The Measurement and Interpretation of Antenna Scattering, Proc IRE vol 37 
pp. 770-777, July, 1949. ' 



The Radar Equation 71 

21. Siegel, K. M.: Far Field Scattering from Bodies of Revolution, Appl. Sci. Research, sec. B, 
vol. 7, pp. 293-328, 1958. 

22. Shosfak, A., and D. Angelakqs: Back-scatter from a Right-circular Cone, Univ. Calif. {Berkeley) 
Electronics Research Lab. Repjt. 70, Office of Naval Research Contract N7onr-29529, July 26, 1957. 

23. Peters, L., Jr.: End-fire Echo Area of Long, Thin Bodies, IRE Trans., vol. AP-6, pp. 133-139, 
January, 1958. / 

24. Crispin, J. W., Jr., R. F. Goodrich, and K. M. Siegel: A Theoretical Method for the Calculation 
of the Radar Cross Sections! of Aircraft and Missiles, Univ. Mich. Radiation Lab. Rept. 2591-1-H 
on Contract AF 19(604)-1949, July, 1959. 

25. Ridenour, L. N. : "Radar Syjstem Engineering," MIT Radiation Laboratory Series, vol. 1, fig. 3.8, 
McGraw-Hill Book Company, Inc., New York, 1947. 

26. Graves, C. D. : Radar Polarization Power Scattering Matrix, Proc. IRE, vol. 44, pp. 248-252, 
February, 1956. j 

27. Pircher, G. : Influence of the Polarization of the Radiated Waves on Radar Detection, Compt. 
rend., vol. 239, pp. 156-1511 Sept. 27, 1954. 

28. Copeland, J. R.: Radar Target Classification by Polarization Properties, Proc. IRE, vol. 48, 
pp. 1290-1296, July, 1960. / 

29. Hiatt, R. E., T. B. A. Senior, and V. H. Weston : A Study of Surface Roughness and Its Effect on 
the Back Scattering Cross Section of Spheres, Proc. IRE, vol. 48, pp. 2008-2016, December, 1960. 

30. Hiatt, R. E., K. M. Siegel, and H. Weil: The Ineffectiveness of Absorbing Coatings on Conducting 
Objects Illuminated by Long Wavelength Radar, Proc. IRE, vol. 48, pp. 1635-1642, September, 
1960. 

31. Hiatt, R. E., K. M. Siegel, and H. Weil: Forward Scattering by Coated Objects Illuminated by 
Short Wavelength Radar, Proc. IRE, vol. 48, pp. 1630-1635, September, 1960. 

32. Schultz, F. V., R. C. Burgener, and S. King: Measurement of the Radar Cross Section of a Man, 
Proc. IRE, vol. 46, pp. 476-481, February, 1958. 

33. Hay, D. R.: The Interpretation of the Radar Cross Section of an Aircraft Model, Symposium on 
Microwave Optics, vol. 1, McGill University, Montreal, June 22-25, 1953. 

34. Swerling, P. : Probability of Detection for Fluctuating Targets, IRE Trans., vol. IT-6, pp. 269-308, 
April, 1960. 

35. Schwartz, M. : Effects of Signal Fluctuation on the Detection of Pulse Signals in Noise, IRE Trans., 
vol. IT-2, pp. 66-71, June, 1956. 

36. Swerling, P. : Detection of Fluctuating Pulsed Signals in the Presence of Noise, IRE Trans., vol. 
1T-3, pp. 175-178, September, 1957. 

37. Sponsler, G. C. : First-order Markov Process Representation of Binary Radar Data Sequences, 
IRE Trans., vol. IT-3, pp. 56-64, March, 1957. 

38. Feller, W.: "An Introduction to Probability Theory and Its Applications, 2d ed.," vol. 1, John 
Wiley & Sons, Inc., New York, 1957. 

39. Cohn, G. I., L. P. Elbinger, and R. M. Leger: Elimination of Ambiguities from High Pulse 
Repetition Rate Radars, Proc. Natl. Electronics Conf., vol. 12, pp. 271-281, 1956. 

40. Cohn, G. I., L. P. Elbinger, and R. M. Leger: Suppression of False Range Indications in High 
Repetition Rate Radars, Proc. Natl. Electronics Conf., vol. 13, pp. 744-760, 1957. 

41. Potter, N. S. : Range Ambiguity Resolution in High PRF Radar, IRE Intern. Conv. Record, vol. 8, 
pt. 8, pp. 65-80, 1960. 

42. Skillman, W. A., and D. H. Mooney : Multiple High-PRF Ranging, Conf. Proc. 4th Natl. Military 
Electronics Conv. (IRE), pp. 37-40, June 27-29, 1960. 

43. Davenport, W. B., Jr.: Signal-to-noise Ratios in Band-pass Limiters, /. Appl. Phys., vol. 24, 
pp. 720-727, June, 1953. 

44. Manasse, R., R. Price, and R. M. Lerner: Loss of Signal Detectability in Band-pass Limiters, 
IRE Trans., vol. IT-4, pp. 34-38, March, 1958. 

45. Varela, A. A.: The Operator Factor Concept, Its History and Present Status, Symposium on 
Radar Detection Theory, ONR Symposium Rept. ACR-10, Mar. 1-2, 1956, AST1A Document 
1 17533. (Quoted with permission of the author.) 

46. Marcum, J. I.: A Statistical Theory of Target Detection by Pulsed Radar, IRE Trans., vo'. IT-6, 
pp. 82-83, April, 1960. 

47. Bussgang, J. J., P. Nesbeda, and H. Safran: A Unified Analysis of Range Performance of CW, 
Pulse, and Pulse Doppler Radar, Proc. IRE, vol. 47, pp. 1753-1762, October, 1959; corrections in 
Proc. IRE, vol. 48, p. 931, May, 1960, and vol. 48, p. 1755, October, 1960. 

48. Meltzer, S. A., and S. Thaler: Detection Range Predictions for Pulse Doppler Radar, IRE Intern. 
Conv. Record, vol. 8, pt. 4, pp. 105-113, 1960. 

49. Polk, C: Optical Fresnel-zone Gain of a Rectangular Aperture, IRE Trans., vol. AP-4, pp. 65-69, 
January, 1956. 

50. Hu, Ming-Kuei: Fresnel Region Field Distributions of Circular Aperture Antennas, IRE Trans., 
vol. AP-8, pp. 344-346, May, 1960. 



3 



CW AND 
FREQUENCY-MODULATED RADAR 



3.1. The Doppler Effect 

A radar detects the presence of objects and locates their position in space by trans- 
mitting electromagnetic energy and observing the returned echo. A pulse radar 
transmits a relatively short burst of electromagnetic energy, after which the receiver is 
turned on to listen for the echo. The echo not only indicates that a target is present, 
but the time that elapses between the transmission of the pulse and the receipt of the echo 
is a measure of the distance to the target. Separation of the echo signal and the 
transmitted signal is made on the basis of differences in time. 

The radar transmitter may be operated continuously rather than pulsed if the strong 
transmitted signal can be separated from the weak echo. The received-echo-signal 
power is considerably smaller than the transmitter power; it might be as little as 10 -18 
that of the transmitted power — sometimes even less. Separate antennas for trans- 
mission and reception help segregate the weak echo from the strong leakage signal, but 
the isolation is usually not sufficient. 

A feasible technique for separating the received signal from the transmitted signal 
when there is relative motion between radar and target is based on recognizing the 
change in the echo-signal frequency caused by the doppler effect. Extremely large 
isolations between antennas are not necessary when the doppler shift in frequency is 
used for detection since the presence of a portion of the transmitted signal in the receiver 
is not, in principle, harmful. In most instances it is a necessity and is required for 
detecting the shift in the echo frequency. 

It is well known in the fields of optics and acoustics that if either the source of oscil- 
lation or the observer of the oscillation is in motion, an apparent shift in frequency will 
result. This i s the doppler effect and is the basis of C W radar. If R is the distance from 
the radar to target, the total number of wavelengths A contained in the two-way path 
between the radar and the target is 2R/L The distance R and the wavelength X are 
assumed to be measured in the same units. Since one wavelength corresponds to an 
angular excursion of 2tt radians, the total angular excursion <j> made by the electro- 
magnetic wave during its transit to and from the target is AnRfX radians. If the target 
is in motion, R and the phase <f> are continually changing. A change in <f> with respect to 
time is equal to a frequency. This is the doppler angular frequency m d , given by 

dj> 4ndR 4nv r .. n 

eo d = 2„/ d =-= T - = — (3.1) 

where f d = doppler frequency shift 

v r = relative (or radial) velocity of target with respect to radar 
The doppler frequency shift is 

f d = 2 J!i r = 2 -^I° (3.2a) 

A C 

where yj, = transmitted frequency 

c = velocity of propagation = 3 x 10 8 m/sec 

72 



Sec. 3.2] CW and Frequency-modulated Radar 73 

If/, is in cycles per second, v r in knots, and X in centimeters, 

f - 103y ' n , M 

/a — — J— (3.2b) 

A plot of this equation is shown in Fig. 3.1. 

The relative velocity may be written v r = v cos d, where v is the target speed and 6 is 
the angle made by the target trajectory and the line joining radar and target. When 
= 0, the doppler frequency is maximum. The doppler is zero when the trajectory is 
perpendicular to the radar line of sight (0 = 90°). 



10,000 



. 1,000 



100 



10 



I 


I ' I I !/ I I I | / T/l I > 


'1 II I) / \ . 


/\ \ y\ \ i4- 


~ 


«///// 




/ - 


- 








JV / // / / 

7/// / / , 
/ / y$/ / / / 












- 




/ - 








= 




/ ~~- 




/ / / /V/ / 
/ / / / y / / 




- 


— / 


/ / / / / V /,s 







- / 


/ // / /yJ' 




2 


s\ 


)/ 1 1 \X\ 1 1 / 1 l/l 1 \A\ 1 1 l ill 


Mill 1 


i i i i i ii 



10 



100 



10,000 



100,000 



1,000 
Radar frequency, Mc 

Fig. 3.1. Doppler frequency [Eq. (3.2ft)] as a function of radar frequency and target relative velocity. 

The type of radar which employs a continuous transmission, either modulated or 
unmodulated, has had wide application. Historically, the early radar experimenters 
worked almost exclusively with continuous rather than pulsed transmissions (Sec. 1.5). 
Two of the more important early applications of the CW radar principle were the 
proximity (VT) fuze and the FM-CW altimeter. The CW proximity fuze was first 
employed in artillery projectiles during World War II and greatly enhanced the effective- 
ness of both field and antiaircraft artillery. The first practical model of the FM-CW 
altimeter was developed by the Western Electric Company in 1938, although the 
principle of altitude determination using radio-wave reflections was known ten years 
earlier, in 1928. 1 

The CW radar is of interest not only because of its many applications, but its study 
also serves as a means for better understanding the nature and use of the doppler 
information contained in the echo signal, whether in a CW or a pulse radar (MTI) 
application. In addition to allowing the received signal to be separated from the 
transmitted signal, the CW radar provides a measurement of relative velocity which may 
be used to distinguish moving targets from stationary objects or clutter. 

3.2. CW Radar 

Consider the simple CW radar as illustrated by the block diagram of Fig. 3.2a. The 
transmitter generates a continuous (unmodulated) oscillation of frequency f , which is 



74 Introduction to Radar Systems 



[Sec. 3.2 



radiated by the antenna. A portion of the radiated energy is intercepted by the target 
and is scattered, some of it in the direction of the radar, where it is collected by the 
receiving antenna. If the target is in motion with a velocity v r relative to the radar, the 
received signal will be shifted in frequency from the transmitted frequency/, by an 
amount ± f d as given by Eq. (3.2). The plus sign associated with the doppler frequency 
applies if the distance between target and radar is decreasing (closing target), that is, 
when the received signal frequency is greater than the (transmitted signal frequency. 
The minus sign applies if the distance is increasing (receding target). The received echo 
signal at a frequency/, ± f d enters the radar via the antenna and is heterodyned in the 
detector (mixer) with a portion of the transmitter signal f to produce a doppler beat 
note of frequency/;. The sign of/ 7 is lost in this process. 

The purpose of the doppler amplifier is to eliminate echoes from stationary targets 
and to amplify the doppler echo signal to a level where it can operate an indicating 
device. It might have a frequency-response characteristic similar to that of Fig. 3.2b. 



AAAAAAA 



f«±f* 



M 



U 



Detector 
(mixer) 



CW 

transmitter 

fo 



Beat -frequency 
amplifier 



Indicator 



Frequency 



Fig. 3.2. (a) Simple CW radar block diagram; 
amplifier. 



(b) response characteristic of beat-frequency 



The low-frequency cutoff must be high enough to reject the d-c component caused by 
stationary targets, but yet it must be low enough to pass the smallest doppler frequency 
expected. Sometimes both conditions cannot be met simultaneously and a com- 
promise is necessary. The upper cutoff frequency is selected to pass the highest 
doppler frequency expected. 

The indicator might be a pair of earphones or a frequency meter. If exact knowledge 
of the doppler frequency is not necessary, earphones are especially attractive provided 
the doppler frequencies lie within the audio-frequency response of the ear. Earphones 
are not only simple devices, but the ear acts as a selective bandpass filter with a passband 
of the order of 50 cps centered about the signal frequency. 2 The narrow-bandpass 
characteristic of the ear results in an effective increase in the signal-to-noise ratio of the 
echo signal. With subsonic aircraft targets and transmitter frequencies in the middle 
range of the microwave frequency region, the doppler frequencies usually fall within the 
passband of the ear. For example, the maximum doppler frequency produced by an 
aircraft with a speed of 600 knots is 6,180 cps when A = 10 cm. If audio detection 
were desired for those combinations of target velocity and transmitter frequency which 
do not result in audible doppler frequencies, the doppler signal could be heterodyned to 



Sec. 3.2] CW and Frequency-modulated Radar 75 

the audible range. The doppler frequency can also be detected and measured by 
conventional frequency meters, usually one that counts cycles. 

An example of the CW radar principle is the radio proximity (VT) fuze, used with 
great success during World War II for the fuzing of artillery projectiles. It may seem 
strange that the radio proximity fuze should be classified as a radar, but it fulfills the 
same basic function of a radar, which is the detection and location of reflecting objects 
by "radio" means. 34 A comparison of the radio-proximity-fuze block diagram (Fig. 
3.3) with the CW radar block diagram (Fig. 3.2) further illustrates the similarity 
between the two. A single tube operating as an oscillating detector acts as both the 
transmitter and the receiver in the radio proximity fuze. The echo signal is detected in 
the plate circuit of the oscillating detector. As with the simple CW radar, the fuze 
doppler amplifier has a frequency-response characteristic corresponding to the expected 
range of doppler frequencies. When the output from the doppler amplifier is of 
sufficient magnitude, the firing circuit, usually a thyratron, is triggered to initiate the 
detonation process. 

Isolation between Transmitter and Receiver. A single antenna serves the purpose of 
transmission and reception in both the proximity fuze and the simple CW radar 
described above. In principle, a single antenna may be employed since the necessary 
isolation between the transmitted and the received signals is achieved via separation in 
frequency as a result of the doppler effect. In practice, it is not possible to eliminate 

Antenna 



7 
















Oscillating 
detector 




Amplifier 




Firing 
circuit 




Detonator 


f>±ft 


fd 







Fig. 3.3. VT fuze block diagram. 

completely the transmitter leakage. However, transmitter leakage is not always 
undesirable. A moderate amount of leakage entering the receiver along with the echo 
signal supplies the reference necessary for the detection of the doppler frequency shift. 
If a leakage signal of sufficient magnitude were not present, a sample of the transmitted 
signal would have to be deliberately introduced into the receiver to provide the necessary 
reference frequency. 

There are two practical effects which limit the amount of transmitter leakage power 
which can be tolerated at the receiver. These are (1) the maximum amount of power 
the receiver input circuitry can withstand before it is physically damaged or its sensitivity 
reduced (burnout) and (2) the amount of transmitter noise due to hum, microphonics 
stray pickup, and instability which enters the receiver from the transmitter. The 
additional noise introduced by the transmitter reduces the receiver sensitivity. Except 
where the CW radar operates with relatively low transmitter power and insensitive 
receivers, as in the proximity fuze, additional isolation is usually required between the 
transmitter and the receiver if the sensitivity is not to be degraded either by burnout or 
by excessive noise. 

The amount of isolation required depends on the transmitter power and the accom- 
panying transmitter noise as well as the ruggedness and the sensitivity of the receiver. 
For example, if the safe value of power which might be applied to a receiver were 10 mw 
and if the transmitter power were 1 kw, the isolation between transmitter and receiver 
must be 50 db. 

The amount of isolation needed in a long-range CW radar is more often determined 
by the noise that accompanies the transmitter leakage signal rather than by any damage 
caused by high power. For example, suppose the isolation between the transmitter and 



76 Introduction to Radar Systems [Sec. 3.2 

receiver were such that 10 mw of leakage signal appeared at the receiver. If the mini- 
mum detectable signal were 10 -13 watt (100 db below 1 mw), the transmitter noise must 
be at least 1 10 db (preferably 130 or 140 db) below the transmitted carrier. 

The transmitter noise of concern in doppler radar includes those noise components 
that lie within the same frequency range as the doppler frequencies. The greater the 
desired radar range, the more stringent will.be the need for reducing the noise modulation 
accompanying the transmitter signal. If complete elimination of the direct leakage 
signal at the receiver could be achieved, it might not entirely solve the isolation problem 
since echoes from nearby fixed targets can also contain the noise components of the 
transmitted signal. 5 

It will be recalled (Sec. 1 .3) that the receiver of a pulsed radar is isolated and protected 
from the damaging effects of the transmitted pulse by a fast-acting switch called the 
TR, which short-circuits the receiver input during the transmission period. Turning 
off the receiver during transmission with a TR-like device is not possible in a CW radar 
since the transmitter is operated continuously. Isolation between transmitter and 
receiver might be obtained with a single antenna by using a hybrid junction, circulator, 
or turnstile junction or with separate polarizations. Separate antennas for trans- 
mitting and receiving might also be used. The amount of isolation which can be 
readily achieved between the arms of practical hybrid junctions such as the magic-T, rat- 
race, or short-slot coupler is of the order of 20 to 30 db. In some instances, when 
extreme precision is exercised, an isolation of perhaps 60 db or more might be achieved. 
One limitation of the hybrid junction is the 6-db loss in over-all performance which 
results from the inherent waste of half the transmitted power and half the received signal 
power. Both the loss in performance and the difficulty in obtaining large isolations 
have limited the application of the hybrid junction to short-range radars. 

Ferrite isolation devices such as the circulator do not suffer the 6-db loss inherent in 
the hybrid junction. Practical devices have isolation of the order of 20 to 50 db. 
Turnstile junctions 6 achieve isolations as high as 40 to 60 db. 

The use of orthogonal polarizations for transmitting and receiving is limited to 
short-range radars because of the relatively small amount of isolation that can be 
obtained. 7 

An important factor which limits the use of isolation devices with a common antenna 
is the reflections produced in the transmission line by the antenna. The antenna can 
never be perfectly matched to free space, and there will always be some transmitted 
signal reflected back toward the receiver. The reflection coefficient from a mis- 
matched antenna with a voltage-standing-wave ratio a is \p\ = (a — 1)/(ct + 1). 
Therefore, if an isolation of 20 db is to be obtained, the VSWR must be less than 1.22. 
If 40 db of isolation is required, the VSWR must be less than 1 .02. 

The largest isolations are obtained with two antennas — one for transmission, the 
other for reception — physically separated from one another. Isolations of the order of 
80 db or more are possible with high-gain antennas. The more directive the antenna 
beam and the greater the spacing between antennas, the greater will be the isolation. 
When the antenna designer is restricted by the nature of the application, large isolations 
may not be possible. For example, typical isolations between transmitting and 
receiving antennas on missiles might be about 50 db at Xband, 70 db at K band, and as 
low as 20 db at L band. 8 

Further isolation may be obtained by introducing a controlled sample of the trans- 
mitter signal directly into the receiver. The phase and amplitude of this signal are 
adjusted to cancel the transmitter signal that leaks into the receiver via the receiving 
antenna. An additional 10 db of isolation or more may be obtained. 9 Another 
method of increasing isolation between separated antennas is with electromagnetic 
absorbing material or metallic baffles placed between the antennas. 10 



Sec. 3.2] 



CW and Frequency-modulated Radar 77 



Although the use of two antennas can provide a high degree of isolation, a loss of 
effective aperture is a consequence. If the area of each of the two antennas is A, the 
total antenna area is 2A. If a single antenna of area 2A were used for both transmission 
and reception, the radar equation (2.1) shows that the single antenna will be capable of 
6 db greater performance (received signal four times greater) than two separate antennas 
of equal total area. In addition to the loss of effective area, the use of two separate 
antennas usually results in a somewhat more difficult mechanical mounting and scanning 
problem than does the single antenna. Nevertheless, these shortcomings may be 
overlooked in many applications, especially if large isolations are necessary and can be 
obtained in no other way. 

Intermediate-frequency Receiver. The receiver of the simple CW radar of Fig. 3.2 
is in some respects analogous to a superheterodyne receiver. Receivers of this type are 
called homodyne receivers, or superheterodyne receivers with zero IF. 11 The function 

Transmitting 



^ c 


CW 








y h 


'o 






' 
















Mixer 




Oscillator 








ht 






' 




'o + 'if, > 


■o-W 








Sideband 
filter 






Receiving 
antenna 


i 


fo+f 

f 


f 














^ 


Receiver 




IF 
amplifier 




2d 
detector 


Doppler 
amplifier 




Indicator 


> 'o * W 


mi 


<er 


f, 


f*'* 




ft 





Fig. 3.4. Block diagram of CW doppler radar with nonzero IF receiver, sometimes called sideband 
superheterodyne. 



of the local oscillator is replaced by the leakage signal from the transmitter. Such a 
receiver is simpler than one with a more conventional intermediate frequency since no 
IF amplifier or local oscillator is required. However, the simpler receiver is not as 
sensitive because of increased noise at the lower intermediate frequencies caused by 
flicker effect. Flicker-effect noise occurs in semiconductor devices such as crystal 
detectors and cathodes of vacuum tubes. The noise power produced by the flicker 
effect varies as l// a , where a is approximately unity. This is in contrast to shot noise 
or thermal noise, which is independent of frequency. Thus, at the lower range of 
frequencies (audio or video region), where the doppler frequencies usually are found, 
the detector of the CW receiver can introduce a considerable amount of flicker noise, 
resulting in reduced receiver sensitivity. For short-range, low-power applications this 
decrease in sensitivity might be tolerated since it can be compensated by a modest 
increase in antenna aperture and/or additional transmitter power. But for maximum 
efficiency with CW radar, the reduction in sensitivity caused by the simple doppler 
receiver with zero IF cannot be tolerated. 

The effects of flicker noise are overcome in the normal superheterodyne receiver by 
using an intermediate frequency high enough to render the flicker noise small compared 
with the normal receiver noise. This results from the inverse frequency dependence of 
flicker noise. Figure 3.4 shows a block diagram of the CW radar whose receiver 
operates with a nonzero IF. Separate antennas are shown for transmission and 



78 



Introduction to Radar Systems 



[Sec. 3.2 



Frequency 
(a) 



HM'- 



vs 



reception. Instead of the usual local oscillator found in the conventional super- 
heterodyne receiver, the local oscillator (or reference signal) is derived in this receiver 
from a portion of the transmitted signal mixed with a locally generated signal of fre- 
quency equal to that of the receiver IF. Since the output of the mixer consists of two 
sidebands on either side of the carrier plus higher harmonics, a narrowband filter selects 
one of the sidebands as the reference signal. This type of receiver is sometimes called 
a sideband superheterodyne. 

In principle, the reference signal could have been generated with a separate local 
oscillator, as in the conventional superheterodyne receiver, if some pains were taken to 
keep the oscillator frequency and the transmitter frequency stable. Only the IF 
frequency oscillator need be kept stable in the configuration shown in Fig. 3.4. Since it 

operates at a lower frequency than would a local oscil- 
lator, the IF oscillator is easier to stabilize than either 
the transmitter or a separate local oscillator. If the 
CW transmitter of the system in Fig. 3.4 drifts slowly 
in frequency, the reference frequency is affected by the 
same drift and the difference frequency (IF) remains 
unchanged, provided the IF oscillator is stable. The 
improvement in receiver sensitivity with an inter- 
mediate-frequency superheterodyne might be as much 
as 30 db over the simple receiver of Fig. 3.2. 

Receiver Bandwidth. One of the requirements of the 
doppler-frequency amplifier in the simple CW radar 
(Fig. 3.2) or the IF amplifier of the sideband super- 
heterodyne (Fig. 3.4) is that it be wide enough to pass 
the expected range of doppler frequencies. In most 
cases of practical interest the expected range of doppler 
frequencies will be much wider than the frequency 
spectrum occupied by the signal energy. Conse- 
quently, the use of a wideband amplifier covering the 
expected doppler range will result in an increase in noise 
and a lowering of the receiver sensitivity. If the fre- 
quency of the doppler-shifted echo signal were known 
beforehand, a narrowband filter — one just wide enough 
to reduce the excess noise without eliminating a sig- 
nificant amount of signal energy — might be used. If the waveform of the echo signal 
were known, as well as its carrier frequency, the matched filter could be specified as 
outlined in Sec. 9.2. 

Several factors tend to spread the CW signal energy over a finite frequency band. 
These must be known if an approximation to the bandwidth required for the narrowband 
doppler filter is to be obtained. 

If the received waveform were a sine wave of infinite duration, its frequency spectrum 
would be a delta function (Fig. 3.5a) and the receiver bandwidth would be infinitesimal. 
But a sine wave of infinite duration and an infinitesimal bandwidth cannot occur in 
nature. The more normal situation is an echo signal which is a sine wave of finite 
rather than infinite duration. The frequency spectrum of a finite-duration sine wave 
has a shape of the form [sin 7r(/-/ )^]M/-/ ), where/ and <5 are the frequency and 
duration of the sine wave, respectively, and /is the frequency variable over which the 
spectrum is plotted (Fig. 3.56). Practical receivers can only approximate this charac- 
teristic. (Note that this is the same as the spectrum of a pulse of sine wave, the only 
difference being the relative value of the duration <5.) In many instances, the echo is 
not a pure sine wave of finite duration but is perturbed by fluctuations in cross section, 



^A 



k^ 



f 

Frequency 
(A) 
Fig. 3.5. Frequency spectrum of 
CW oscillation of (a) infinite 
duration and (b) finite duration. 



Sec. 3.2] CW and Frequency-modulated Radar 79 

target accelerations, scanning fluctuations, etc., which tend to broaden the bandwidth 
still further. Some of these spectrum-broadening effects are considered below. 

Assume a CW radar with an antenna beamwidth of 8 B deg scanning at the rate of & s 
deg/sec. The time on target (duration of the received signal) is 6 = 6 B j6 s sec. Thus 
the signal is of finite duration and the bandwidth of the receiver must be of the order of 
the reciprocal of the time on target 6J6 B . Although this is not an exact relation, it is a 
good enough approximation for purposes of the present discussion. If the antenna 
beamwidth were 2° and if the scanning rate were 36°/sec (6 rpm), the spread in the 
spectrum of the received signal due to the finite time on target would be equal to 18 cps, 
independent of the transmitted frequency. 

It has sometimes been stated that the width of the frequency spectrum due to the 
finite time on target corresponds to the doppler frequency that would be produced by 
the velocity of the periphery of the rotating antenna. 9 Although this may be approxi- 
mately true for a mechanically scanning antenna, it appears to be a fortuitous result with 
no physical significance. The following is a qualitative argument to justify such a 
conclusion. 

The width of the received signal spectrum (1/5) is equal to 6jd B . The beamwidth of a 
reflector- type antenna such as a paraboloid of diameter D is given by 6 B = kljD, where 
X is the wavelength. The constant k depends upon the manner in which the reflector is 
illuminated. For practical reflector antennas, k might vary from 60 to 80, with 65 a 
typical value, when B is measured in degrees. The peripheral velocity of the antenna 
is v v = s Dl(2 X 57.2), where v v is in feet per second, 6 S in degrees per second, and D in 
feet. From the above relationships the approximate width of the spectrum is therefore 

1 _ 6 S _ (0.88)2t>. fl 
6 6 B A 

This is approximately equal to the doppler frequency shift (f d = 2vJX) of an object 
moving at a speed equal to the peripheral velocity of the antenna. The similarity is 
claimed to be fortuitous. 

Perhaps the most significant reason for stating that no causal relation exists between 
the spread in frequency and the mechanical motion of the antenna is that the scanning 
beam need not be generated by mechanically moving a reflector antenna. An antenna 
consisting of an array of elements can be scanned by electrically controlling the phase 
shift in each element (Sec. 7.7). No part of the antenna is physically in motion, but the 
spread in spectrum nevertheless exists, just as with a mechanically rotating antenna, 
because of the finite time on target. A similar argument applies to a target flying 
through the beam of a stationary antenna. 

In addition to the spread of the received signal spectrum caused by the finite time on 
target, the spectrum may be further widened if the target cross section fluctuates. The 
fluctuations widen the spectrum by modulating the echo signal. In a particular case, it 
has been reported 9 that the aircraft cross section can change by 1 5 db for a change in 
target aspect of as little as J°. If, for some reason, the target aspect were to change at 
the rate of 10°/sec (perhaps a deliberate target maneuver or flight instabilities), the echo 
signal would be modulated at a rate as high as 15 cps. A modulation of this amount 
might necessitate an increased receiver bandwidth if it were large compared with the 
spectral bandwidth of the transmitted signal. 

The echo signal from a propeller-driven aircraft can also contain modulation com- 
ponents at a frequency proportional to the propeller rotation. 12 The spectrum 
produced by propeller modulation is more like that produced by a sine-wave signal and 
its harmonics rather than a broad, white-noise spectrum. The frequency range of 
propeller modulation depends upon the shaft-rotation speed and the number of 
propeller blades. It is usually in the vicinity of 50 to 60 cps for World War II aircraft 



80 Introduction to Radar Systems [Sec. 3.2 

engines. This could be a potential source of difficulty in a CW radar since it might 
mask the target's doppler signal or it might cause an erroneous measurement of doppler 
frequency shift. In some instances, propeller modulation can be of advantage. It 
might permit the detection of propeller-driven aircraft passing on a tangential trajectory, 
even though the doppler frequency shift is zero. 

If the target's relative velocity is not constant with time but is changing, a further 
widening of the received signal spectrum can occur. The change in relative velocity Av r 
over a time At is equal to a r At, where a r is the acceleration of the target with respect to 
the radar. The change in velocity causes a change in doppler frequency Af d equal to 

. , 2 Ay. 2a r At 
J X X 

A filter of bandwidth Af d will just accommodate this change in frequency (assuming all 
other band-widening factors to be negligible). The response time, or build-up time, of 
a filter of bandwidth Af a is approximately 1 jAf d . Since the time At in which the doppler 
changes frequency by an amount Af d should not be less that the filter build-up time, the 
required receiver bandwidth is 

= 2a r At = 2a r (llAf d ) 
U X X 

or Af a = {^Y (3.3 fl ) 

If a r is in feet per second per second and X in centimeters, then 

If the target performs a 2g maneuver — a moderate maneuver for a military fighter 
aircraft but a large maneuver for a commercial aircraft — the receiver bandwidth must 
be approximately 20 cps when the transmitted wavelength is 10 cm. 

The composite effect of the various spectrum-widening factors is difficult to predict. 
If the received waveform were exactly known, it would be possible, in theory, to 
compute the shape of the receiver characteristic which maximizes the signal-to-noise 
ratio by the matched-filter theory of Sec. 9.2. However, the exact shape of the received 
waveform is not likely to be known, and even if it were, there is no assurance that a 
proper matched filter could be readily constructed. Therefore approximate methods 
must ordinarily be used to obtain the filter characteristic. In the event the various 
effects were all of equal magnitude, the receiver bandwidth could be approximated by 
the rms value of the individual bandwidths. If one effect were much larger than all the 
rest, obviously the other factors could be neglected and the receiver characteristic 
determined by the dominant factor. 

In many cases, the doppler frequency shift may not be known precisely. When the 
band in which the doppler frequencies are expected is known, the receiver passband may 
be widened to include the entire range of expected doppler frequency. Although the 
received echo signal will then fall somewhere within the receiver bandwidth, the 
increased bandwidth results in increased noise and reduced sensitivity. Furthermore, 
all knowledge of the exact value of doppler velocity is lost. 

When the doppler-shifted echo signal is known to lie somewhere within a relatively 
wide band of frequencies, a bank of narrowband filters spaced throughout the frequency 
range permits a measurement of frequency and improves the signal-to-noise ratio. 
These filters can be in either the RF, IF, or video portion of the receiver. The filter 
bank diagramed in Fig. 3.6 is at IF. The bandwidth of each individual filter is wide 
enough to accept the signal energy, but not so wide as to introduce more noise than need 



Sec. 3.2] 



CW and Frequency-modulated Radar 81 



be. The center frequencies of the filters are staggered to cover the entire range of 
doppler frequencies. If the filters are spaced with their half-power points overlapped, 
the maximum reduction in signal-to-noise ratio of a signal which lies midway between 
adjacent channels compared with the signal-to-noise ratio at midband is 3 db. The 
more niters used to cover the band, the less will be the maximum loss experienced, but 
the greater the probability of false alarm. 

A bank of narrowband filters may be used after the detector in the video of the simple 
CW radar of Fig. 3.2 instead of in the IF. The improvement in signal-to-noise ratio 
with a video filter bank is not as good as can be obtained with an IF filter bank, but the 
ability to measure the magnitude of doppler frequency is still preserved. Because of 



.— ► Filter No.2 



Mixer 



IF 
amplifier 



Filter No. 1 — Det. 



Filter No. 3 — Det. -*, I— 



» Filter No. 4 — Det. 



* Filter Na/2 — Det. 




(a) 




f\ h h U 
Frequency 

(b) 



(b) frequency-response characteristic of 



Fig. 3.6. (a) Block diagram of IF doppler filter bank; 
doppler filter bank. 

foldover, a frequency which lies to one side of the IF carrier appears, after detection, at 
the same video frequency as one which lies an equal amount on the other side of the IF. 
Therefore the sign of the doppler shift is lost with a video filter bank, and it cannot be 
directly determined whether the doppler frequency corresponds to an approaching or 
to a receding target. (The sign of the doppler may be determined in the video by other 
means, as described later.) One advantage of the foldover in the video is that only half 
the number of filters are required than in the IF filter bank. There are many techniques 
which may be used to achieve narrowband IF filters. Mechanical filters and crystal 
filters are two possibilities. A simple video filter bank may be obtained with vibrating 
reeds in which detection and measurement are accomplished by visual observation. 

A bank of overlapping doppler filters, whether in the IF or video, increases the 
complexity of the receiver. When the system requirements permit a time sharing of the 
doppler frequency range, the bank of doppler filters may be replaced by a single narrow- 
band tunable filter which searches in frequency over the band of expected doppler 
frequencies until a signal is found. After detecting and recognizing the signal, the 
filter may be programmed to continue its search in frequency for additional signals. 
One of the techniques for accomplishing this is similar to the tracking speed gate 
described in Sec. 5.7 or to the phase-locked filter. 13 



fo 
Frequency 

la) 



t! 



82 Introduction to Radar Systems [Sec. 3.2 

If, in any of the above techniques, moving targets are to be distinguished from 
stationary objects, the zero-doppler-frequency component must be removed. The 
zero-doppler-frequency component has, in practice, a finite bandwidth due to the finite 
time on target, clutter fluctuations, and equipment instabilities. The clutter-rejection 
band of the doppler filter must be wide enough to accommodate this spread. In the 
multiple-filter bank, removal of those filters in the vicinity of the RF or IF carrier 
removes the stationary- target signals . In the wideband I F where a bank of filters is not 
used, it would be necessary to center a rejection band about the IF frequency in order to 

remove stationary targets. The low-frequency cutoff in the 
video filter characteristic of the simple CW radar (Fig. 3.2b) 
also serves to remove the energy of fixed clutter concen- 
trated in a finite spectrum about zero frequency. 

Sign of the Radial Velocity. In some applications of 
CW radar it is of interest to know whether the target is 
approaching or receding. This might be determined with 
separate filters located on either side of the intermediate 
frequency. If the echo-signal frequency lies below the car- 
rier, the target is receding; if the echo frequency is greater 
than the carrier, the target is approaching (Fig. 3.7). The 
direction of target motion may also be found from the 
change in amplitude of the received signal with time. 
However, this is not always a satisfactory method, since the 
echo signal does not vary rapidly with range except at short 
ranges. A relatively long observation time is necessary to. 
reliably detect a significant change. Furthermore, within 
the observation interval, variations in the amplitude of the 
echo signal from a complex target can be considerably 
greater than the change in amplitude due to the change in 
range. 

The direction of target motion might be determined by 
measuring the doppler frequency as a function of time and 
observing whether the frequency is increasing or decreasing. 
This also requires a relatively long time in which to make 
observations. 

Although the doppler-frequency spectrum "folds over" in 
the video because of the action of the detector, it is possible to determine its sign from 
a technique, known as the phasing method, borrowed from single-sideband communi- 
cations. If the transmitter signal is given by 

E t = E cos m t 

the echo signal from a moving target will be 



Frequency 
16) 



n 



Frequency 
(c) 

Fig. 3.7. Spectra of received 
signals, (a) No doppler 
shift, no relative target 
motion ; (b) approaching 
target; (c) receding target. 



(3.4) 



E r = k x E cos [(m ± m d )t + </>] 



(3.5) 



where 



E 
k, 



amplitude of transmitter signal 
a constant determined from the radar equation 
co = angular frequency of transmitter, radians/sec 
<o d = doppler angular frequency shift 

(f> = a constant phase shift, which depends upon range of initial detection 
The sign of the doppler frequency, and therefore the direction of target motion, may be 
found by splitting the received signal into two channels as shown in Fig. 3.8. In 
channel A the signal is processed as in the simple CW radar of Fig. 3.2. The received 



Sec. 3.2] 



CW and Frequency-modulated Radar 



83 



signal and a portion of the transmitter heterodyne in the detector (mixer) to yield a 
difference signal 

E A = k 2 E cos (±w d t + 4>) (3.6) 

The other channel is similar, except for a 90° phase delay introduced in the reference 
signal. The output of the channel B mixer is 

E B = k 2 E cos [±o> d t + <f> + y (3.7) 

If the target is approaching (positive doppler), the outputs from the two channels are 

E A (+) = fc 2 £o cos (m d t + <j>) E B (+) = k 2 E cos (m a t + <f> + A (3.8a) 

On the other hand, if the targets are receding (negative doppler), 

E A (~) = k 2 E cos (w d t - <j>) E B (-) = k 2 E cos ico d t - <f> - - J (3.8i>) 

The sign of a> d and the direction of the target's motion may be determined according to 
whether the output of channel B leads or lags the output of channel A . One method of 

Transmitting 
antenna 



>j 








CW 






y 




transmitter 














• 




' 






90" 
phase 
shift 
















Mixer 
A 






Receiving 




Channel A 






antenna 










Synchronous 

motor 

indicator 


s » 






• 




y 




■ 


Channel B 








Mixer 










L 


i 







Fig. 3.8. Measurement of doppler direction using synchronous, two-phase motor. 

determining the relative phase relationship between the two channels is to apply the 
outputs to a synchronous two-phase motor. 14 The direction of motor rotation is an 
indication of the direction of the target motion. 

An electronic technique for measuring the relative phase between the two signals is 
shown in Fig. 3.9. This has been used in a rate-of-climb meter for vertical take-off 
aircraft to determine the velocity of the aircraft with respect to the ground during 
take-off and landing. 15 To simplify the description of operation, a separate antenna is 
shown in Fig. 3.9 for both transmission and reception, although a single antenna can be 
employed if proper duplexing means are used. The received signal is divided into two 
channels (A and B) and fed into separate detectors. A portion of the transmitter signal 
is fed directly into the detector of channel A. In channel B, the reference from the 
transmitter is delayed 90°. Therefore a 90° phase shift is introduced between the 



84 



Introduction to Radar Systems 



[Sec. 3.2 



doppler beat notes in the two channels. The sign of the phase shift determines the 
direction of motion, as in the system of Fig. 3.8. 

To determine the sign of the 90° phase shift, the two signals are first amplified and 
limited. Figure 3.9* shows the limited waveforms (1 and 2). The waveform from 
limiter B is differentiated (3) and also inverted (4). The output from limiter ,4(1) and 
the differentiated output of B (3) are compared in the coincidence circuit labeled the 
upgate. If both signals 1 and 3 are positive, a pulse will be generated (5) from the 
upgate to indicate a receding target. In the rate-of-climb meter a receding target is one 
which is ascending. Approaching targets produce no output from the upgate coinci- 
dence circuit. A similar comparison in a coincidence circuit, called the downgate, of 

Rate-of-climb meter 




(a) 



( 1 ) Limiter A T 

(2) Limiter 8 



i r 



r 



(3) Differentiation 
of B 



(b) 



(4) Inversion of B 



(5) Up gate » 

[coincidence — '*- 
of (3)and(1 )] 



(6) Down gate 
[coincidence 
of (4)and(1)] 



Fig. 3.9. Measurement of doppler direction as used for VTO aircraft rate-of-climb meter. (After 
Logue, l& Electronics.) J 

limiter A output (1) with the output of the inverting circuit (4) will indicate approaching, 
but not receding, targets. The pulses from the two coincidence circuits are counted and 
displayed on a zero-center-scale microammeter, which indicates direction as well as 
magnitude of the doppler frequency. 

Derivation of Doppler Frequency Shift. The effect of a moving target on the frequency 
and phase of the radar echo may be derived from simple considerations of the voltage 
waveforms, taking account of the time delays in the transit of the energy from the radar 
to the moving target and back. The form of the transmitted signal is taken to be 

sin (cv + <f>o) (3.9) 

where <f> is an arbitrary phase shift. The amplitude of the transmitted signal waveform, 
as well as all other waveforms considered here, is assumed to be unity, since it is the 
argument of the sine factor and not the amplitude which is of importance in deriving the 
doppler frequency shift. Assume, initially, that the target is stationary at a distance R 
from the radar. The time taken in traveling from the radar to the target is R /c, where c 
is the velocity of propagation. The signal received at the stationary target is the same 



CW and Frequency-modulated Radar 



85 



Sec. 3.2] 

as that which was transmitted by the radar a time R jc in the past. Therefore the signal 
at the target is 

sin Wo ^ _ <j + fa = S i n (a, ot _ ^S + ^ (3.10) 

The echo signal back at the radar is the same as the signal at the target a time RJc 
earlier than Eq. (3.10) and is 



sin 



(«* - 2 -^-° + A,) 



(3.11) 



If the target is in motion with respect to the radar, the distance will not be constant, 
but will vary with time. The signal at the moving target may be written 



sin \cd 



R(t) 



] + 4>o) 



(3.12) 



where the distance R(t) is a function of time. If the velocity of the target with respect to 
the radar is v r , and if the acceleration may be taken to be zero, the distance to the target 

R(t) = R T v r (t - g (3-13) 

where R is the distance between radar and target at the time t = t . The minus sign 
associated with v r applies for a target approaching the radar, while the plus sign applies 
to a receding target. Substituting Eq. (3.13) into Eq. (3.12) gives the signal from the 
radar at a moving target as 



sin \co 



t-^±^(t 
c c 



Q 



+ <f>o\ = sin 



w (l±^)f-^ (R ±Vo) + <£o 



(3.14) 

The echo signal received back at the radar at any instant of time is the same as the 
signal that was at the target a time R{t)jc earlier. Consequently, the received echo 
signal from a moving target may be written 



sin «„ 



r — 



2R(tj 



c J 



+ <t>o\ = sin 



*('±*?)' 



C 



4>0 



Since co d = 2a> v r /c, the received echo signal becomes 



sin 



(ft>o ± <»d)t ~ -^ 2 - 2 T m a t + <£ 



(3.15) 



(3.16) 



Thus the moving-target echo is shifted in frequency by the amount ± co d and in phase by 
^co d t as compared with the signal that would have been received from a stationary 
target [Eq. (3.11)]. 

Advantages and Limitations of CW Radar. When used for the detection of targets at 
short and moderate ranges, the CW radar is characterized by simpler equipment than a 
pulse radar of equivalent detection (range) capability. The difference between CW 
and pulse-radar techniques may be likened to the difference between radio and TV 
techniques. 9 The simple CW radar, however, is not capable of determining range, as is 
the conventional pulse radar. The receiver bandwidth of CW radar is usually measured 
in terms of kilocycles or less, whereas the typical pulse-radar receiver bandwidth is 
measured in terms of megacycles. The high-voltage modulator needed to pulse a power 
tube is not found in a CW radar. Peak power is less in the CW radar since the duty 
cycle is unity. Electrical breakdown as a result of high peak power is usually not a 



86 Introduction to Radar Systems [Sec. 3.3 

factor in equipment design as it might be with pulse radar. The average transmitter 
power, however, is of comparable magnitude in CW and pulse radars, for equivalent 
detection capability. CW transmitters are smaller in size and weight than comparable 
pulse transmitters. In a typical application, the CW transmitter can be 25 to 50 per 
cent as heavy as a corresponding pulse transmitter. 

A CW radar can operate, in principle, against targets down to almost zero range. 
The minimum range of a pulse radar depends on the extent of the pulse in space and the 
duplexer recovery time. Since the CW radar uses the doppler frequency shift for 
detection, it permits moving targets to be discriminated from stationary objects 
(clutter). A pulse radar also may be made to discriminate between moving targets and 
stationary objects by use of the doppler effect. Such a radar, called MTI radar, is more 
complicated than the simple pulse radar. Both the CW radar and the pulse MTI radar 
are blind to targets with zero or small relative velocities, even though the magnitude of 
the vector velocity might be large. Small or zero relative velocities occur for targets 
whose paths are perpendicular to the radar beam, that is, tangent or crossing trajectories. 

The simple CW radar is usually a single-target device. Its ability to handle multiple 
targets can be increased by providing resolution in the doppler-frequency domain as 
with a bank of narrowband doppler filters. The number of targets that the radar can 
resolve at any one time is equal to the number of doppler filters. 

There is a practical limit to the amount of power that can usefully be employed with a 
CW radar. The power limitation is different from that in the pulse radar, since in a 
CW radar the maximum power is dependent upon the amount of isolation and the 
transmitter noise. The transmitter noise that finds its way into the receiver degrades 
the receiver sensitivity. The pulse radar has no similar limitation to its maximum 
range because the transmitter is not operative when the receiver is turned on. 

Perhaps one of the greatest shortcomings of the simple CW radar is its inability to 
obtain a measurement of range. This limitation can be overcome by increasing the 
bandwidth of the transmitted signal as with frequency modulation or by transmitting 
two or more frequencies simultaneously. 

In spite of its limitations, CW radar has found wide application, especially where the 
measurement of velocity is important. Its use in the radio proximity fuze and as a 
rate-of-climb meter for VTO (vertical take-off) aircraft has already been mentioned. A 
few of the other typical applications to which the CW radar has been applied include the 
detection of tornadoes, the measurement of railroad-freight-car velocity to control 
humping operations, 16 and as an aircraft navigation aid (Sec. 3.4). Perhaps the 
application of closest concern to the reader is its use as a radar speed meter extensively 
employed by traffic-enforcement agencies. 17-19 

3.3. Frequency-modulated CW Radar 

The inability of the simple CW radar to measure range is related to the relatively 
narrow spectrum (bandwidth) of its transmitted waveform. Some sort of timing mark 
must be applied to a CW carrier if range is to be measured. The timing mark permits 
the time of transmission and the time of return to be recognized. The sharper or more 
distinct the timing mark, the more accurate the measurement of the transit time. But 
the more distinct the timing mark, the broader will be the transmitted spectrum. This 
follows from the properties of the Fourier transform. Therefore a finite spectrum must 
of necessity be transmitted if transit time or range is to be measured. 
•>( The spectrum of a CW transmission can be broadened by the application of modula- 
tion, either amplitude, frequency, or phase. An example of an amplitude modulation 
is the pulse radar. The narrower the pulse, the more accurate the measurement of 
range and the broader the transmitted spectrum. A widely used technique to broaden 
the spectrum of CW radar is to frequency-modulate the carrier. The timing mark is 



Sec. 3.3] 



CW and Frequency-modulated Radar 87 



the changing frequency. The transit time is proportional to the difference in fre- 
quency between the echo signal and the transmitter signal. The greater the transmitter 
frequency deviation in a given time interval, the more accurate the measurement of the 
transit time and the greater will be the transmitted spectrum. 

Range and Doppler Measurement. In the frequency-modulated CW radar (abbrevi- 
ated FM-CW), the transmitter frequency is changed as a function of time in a known 
manner. Assume that the transmitter frequency increases linearly with time, as shown 
by the solid line in Fig. 3.10a. If there is a reflecting object at a distance R, an echo 
signal will return after a time T = 2R/c. The dashed line in the figure represents the 




2±Zi 



z^z: 



Time 



<£•) 



Fig 3.10. Frequency-time relationships in FM-CW radar. Solid curve represents transmitted signal; 
dashed curve represents echo, (a) Linear frequency modulation ; (6) triangular frequency modulation ; 
(c) beat note of (6). 

echo signal. If the echo signal is heterodyned with a portion of the transmitter signal 
in a nonlinear element such as a crystal diode, a beat note/ 6 will be produced. If there 
is no doppler frequency shift, the beat note (difference frequency) is a measure of the 
target's range and/; =/ r , where f r is the beat frequency due only to the target's range. 
If the rate of change of the carrier frequency is/ , the beat frequency is 



fr=JoT= 2 -^fo 



(3.J7) 



In any practical CW radar, the frequency cannot be continually changed in one 
direction only. Periodicity in the modulation is necessary, as in the triangular- 
frequency-modulation waveform shown in Fig. 3.10Z>. The modulation need not 
necessarily be triangular; it can be sawtooth, sinusoidal, or some other shape. The 
resulting beat- frequency as a function of time is shown in Fig. 3.10c for triangular 
modulation. The beat note is of constant frequency except at the turn-around region. 
If the frequency is modulated at a rate/ m over a range A/, the beat frequency is 

c c 

Thus the measurement of the beat frequency determines the range R. 



88 



Introduction to Radar Systems 



[Sec. 3.3 

A block diagram illustrating the principle of the FM-C W radar is shown in Fig. 3 . 1 1 . 
A portion of the transmitter signal acts as the reference signal required to produce the 
beat frequency. It is introduced directly into the receiver via a cable or other direct 
connection. Ideally, the isolation between transmitting and receiving antennas is 
made sufficiently large so as to reduce to a negligible level the transmitter leakage signal 
which arrives at the receiver via the coupling between antennas. The beat frequency is 
amplified and limited to remove any amplitude fluctuations. The frequency of the 
amplitude-limited beat note is usually measured with a cycle-counting frequency meter 
calibrated in distance. 



Transmitting 
antenna 



?! < 




FM 




— < — 








J 


transmitter 






Receiving 
antenna 




' Referenc 


e sig 


nal 














."> » 


■ 


— > — 


Amplifier 


— » — 


Limiter 


> 


Frequency 
counter 


> 


Indicator 


) ' 







Fig. 3.11. Block diagram of FM-CW radar. 

In the above, the target was assumed to be stationary. If this assumption is not 
applicable, a doppler frequency shift will be superimposed on the FM range beat note 
and an erroneous range measurement results. The doppler frequency shift causes the 
frequency-time plot of the echo signal to be shifted up or down (Fig. 3.12a). On one 
portion of the frequency-modulation cycle, the beat frequency (Fig. 3.126) is increased 
by the doppler shift, while on the other portion, it is decreased. If, for example, the 
target is approaching the radar, the beat frequency f b (up) produced during the increas- 
ing, or up, portion of the FM cycle will be the difference between the beat frequency 



Transmitted signal 
Received signal 




5sS> 



±±J- 



fr+fd 



^ 



=£ 



^ 



[b) 



Time 



Fig. 3.12. Frequency-time relationships in FM-CW radar when the received signal is shifted in 
frequency by the doppler effect, (a) Transmitted (solid curve) and echo (dashed curve) frequencies; 
(J>) beat frequency. 

due to the range/, and the doppler frequency shift/, [Eq. (3.19a)]. Similarly, on the 
decreasing portion, the beat frequency/, (down) is the sum of the two [Eq. (3.196)]. 

/»("P)=/r-/i (3.19a) 

/ 6 (down) =/,+/* (3.196) 

The range frequency/ may be extracted by measuring the average beat frequency; 

that is, \[f h (up) +/, (down)] =/. If/, (up) and/, (down) are measured separately, 

for example, by switching a frequency counter every half modulation cycle, one-half 

the difference between the frequencies will yield the doppler frequency. This assumes 



Sec. 3.3] CW and Frequency-modulated Radar 89 

/r > fa- If> on tne otner hand,y^ < f d , such as might occur with a high-speed target at 
short range, the roles of the averaging and the difference-frequency measurements are 
reversed; the averaging meter will measure doppler velocity, and the difference meter, 
range. If it is not known that the roles of the meters are reversed because of a change in 
the inequality sign between f r and/j, an incorrect interpretation of the measurements 
may result. 

When more than one target is present within the view of the radar, the mixer output 
will contain more than one difference frequency. If the system is linear, there will be a 
frequency component corresponding to each target. In principle, the range to each 
target may be determined by measuring the individual frequency components and 
applying Eq. (3.18) to each. To measure the individual frequencies, they must be 
separated from one another. This might be accomplished with a bank of narrowband 
filters, or alternatively, a single frequency corresponding to a single target may be 
singled out and continuously observed with a narrowband tunable filter./ But if the 
motion of the targets were to produce a doppler frequency shift, or if the frequency- 
modulation waveform were nonlinear, or if the mixer were not operated in its linear 
region, the problem of resolving targets and measuring the range of each becomes more 
complicated. In many cases the advantages of the multiple-target FM-CW radar do 
not outweigh the practical difficulties inherent in its realization, and consequently little 
or no application of the FM radar in this mode of operation seems to have been made. 

If the FM-CW radar is used for single targets only, such as in the radio altimeter, it 
is not necessary to employ a linear modulation waveform. / This is certainly advantage- 
ous since a sinusoidal or almost sinusoidal frequency modulation is easier to obtain with 
practical equipments than are linear modulations. The beat frequency obtained with 
sinusoidal modulation is not constant over the modulation cycle as it is with linear 
modulation. However, it may be shown that the average beat frequency measured 
over a modulation cycle, when substituted into Eq. (3.18), yields the correct value of 
target range. 

Assume the transmitted signal to be sinusoidally modulated with a voltage waveform 

v t = V t sin (2*/ * + ^f sin 2vfJ\ (3.20) 

^ Aim 

The voltage received from the target is delayed by a time T = 2R/c and may be written 

(3.21) 



v r = V r sin 



2nUt -T)+£f sin 27rf m (t - T) 

Aim 



The received signal [Eq. (3.21)] and the transmitted signal [Eq. (3.20)] are heterodyned 
in a mixer to give a difference-frequency signal of 



v b = kV t V T sin (^ sin (tf m T) cos 2nf m (* - |) 



„. +2nf„T\ (3.22) 

J m 

where A: is a constant of proportionality. Since T < l// m , we may write 

sin Trf m T «a -n-f m T, 

and — sin nf m T s» -n A/T 

J m 

Therefore the voltage waveform of the difference-frequency signal becomes 

Vh = k V t F r [sin 2nf T + it AfT cos (2w/ m / - Ttf m T)\ (3 .23) 



90 Introduction to Radar Systems 



[Sec. 3.3 



The frequency may be found by differentiating the argument of Eq. (3.23) with respect 
to time. 

/«. = - f (* A/TX277/-J sin (2nf m t - 7rf m T) = 77 AfTf m sin {2nf m t - nf m T + tt) 

(3.24) 

The minus sign obtained from differentiation of the cosine is equivalent to a phase shift 
of 77 radians. The average of the beat frequency over one-half a modulating cycle is 

fb = TnT n A/T/m Sin (277/m/ ~ ^» T + *)dt = n A// m Tcos irf m T (3.25) 

Since f m T<4 1 and cos nf m T & 1, 



f b = 2Aff m T=; A MnM = fr 



(3.26) 



Although the above example assumed the modulation waveform to be sinusoidal, it 
can be shown that any reasonable-shape modulation waveform can be used to measure 













/ ' J\ ^ 


ft 


\ N 




/ / -£\ \-33 


1 1 


\ \ 




O \ \ » 


/ / 






\r> \ \ to 


/ / 






3\ \« 








"SA \«a. 

\ ^^o 


/ / 
/ / 
/ / 


A 


f 




/ / 
/ / 










' 







Time — *■ 
Fig. 3.13. Example of a practical frequency-modulation waveform. (From Capelli, 22 IRE Trans.) 

the range, provided the average beat frequency is measured. 20 - 21 If the target is in 
motion and the beat signal contains a component due to the doppler frequency shift, the 
range frequency can be extracted as before, if the average frequency is measured. To 
extract the doppler frequency, the modulation waveform must have equal upsweep and 
downsweep time intervals. 

FM Radar Equipment. One of the major applications of the FM-CW radar principle 
has been as an altimeter on board aircraft to measure height above the earth. The large 
target cross section and the relatively short ranges required of altimeters permit low 
transmitter power and low antenna gain. Since the relative motion, and hence the 
doppler velocity between the aircraft and ground, is small, the effect of the doppler 
frequency shift may usually be neglected. 

At UHF frequencies (up to 1 or 2 Gc) the triode can supply the necessary transmitter 
power. However, at frequencies greater than several gigacycles, either the klystron 
(reflex oscillator or amplifier) or the CW magnetron may be used. Backward-wave 
oscillators might also be used. The reflex klystron offers the advantage that it can be 
electronically frequency-modulated by changing the reflector voltage. CW magnetrons 
may be electronically frequency-modulated, or they may be mechanical-modulated by 
vibrating an internal reed assembly which varies the capacity across the straps of the 
anode cavity. If the vibrating reed assembly had no mass, a driving voltage with 
triangular waveform could produce a frequency modulation with the desired triangular 
shape. However, the reed does have mass, and its inertia causes a rounding of the 



Sec. 3.3] CW and Frequency-modulated Radar 91 

frequency modulation if a triangular driving voltage is applied. Mechanical reso- 
nances in the vibrating reed will further distort the waveform. Although proper shaping 
of the driving voltage minimizes the effects of mechanical resonances and inertia, some 
distortions still occur. 21 

The distortions in the frequency-modulation waveform caused by mechanical inertia 
do not exist in an oscillator which is electronically modulated. Unfortunately, most 
practical devices which can be readily frequency-modulated by electronic means also 
produce undesirable amplitude modulation as a consequence. It seems, therefore, 
that the achievement of a perfectly linear triangular frequency modulation is a difficult 
task. In practice, a rounded turnover cannot seem to be avoided. An example of 
a practical frequency-modulation curve is shown in Fig. 3.13; the modulation is 
linear approximately 60 per cent of the time. 22 The exact shape of the modulation 
waveform is not important so long as only a single target is within the view of the radar 
and if the beat frequency is averaged over a modulation cycle. 

The parameters of a typical FM radar altimeter, the AN/APN-22, are given in Table 
3.1. 

Table 3.1. Characteristics of the AN/APN-22 Radar Altimeter t 

Frequency 4,200-4,400 Mc 

Transmitter power 1.5 watts 

Frequency excursion Af 70 Mc 

Modulation frequency f m 120 cps 

Antenna beamwidth 60° 

Range : 

Over land 0-10,000 ft 

Over water 0-20,000 ft 

Accuracy: 

0-40 ft ±2 ft 

40-20,000 ft ±5% 

Transmitter Mechanically modulated CW magnetron 

t Wimberly and Lane. 23 

The receivers employed in FM-CW radars are similar to those of the simple CW radar 
discussed earlier in this chapter. In its simplest form, the receiver might consist of a 
crystal mixer followed by a low-frequency amplifier and a frequency-measuring device. 
This is similar to the conventional crystal video receiver except for the presence of the 
reference signal necessary to extract the difference frequency and the range. The 
function of the reference signal can be performed by the transmitter leakage. A better 
technique for introducing the reference signal in the receiver is by direct connection, as 
was shown in Fig. 3.11. The direct connection permits better control of the magnitude 
of the reference signal, and as a result, the crystal mixer can be made to operate more 
efficiently. Too little or too much reference signal lowers the sensitivity of the receiver, 
just as too little or too much oscillator power degrades the sensitivity of a superhetero- 
dyne receiver. The error in range due to the separation of transmitter and receiver can 
be more readily compensated for if the reference signal is introduced into the receiver 
via a known length of cable rather than an unknown length of leakage path. 

Another advantage of supplying the reference signal by a direct connection is that 
transmitter noise may be reduced with a balanced mixer (Sec. 8.8). Even though the 
transmitter noise may be considerably reduced in the direct reference signal, the ultimate 
performance will be determined by the unavoidable leakage signal and its noise com- 
ponents which find their way into the receiver by way of antenna coupling or by reflec- 
tions from nearby objects. The noise which accompanies the leakage signal may be 
reduced by improving the isolation between the transmitting and the receiving antennas. 
There is, however, a practical limit to the amount of isolation which can be achieved. 
A typical installation of a radar altimeter with separated receiving and transmitting 



92 Introduction to Radar Systems 



[Sec. 3.3 



antennas on an aircraft might provide 65 to 70 db of isolation. 24 Further isolation 
may be obtained by proper adjustment of the phase and amplitude of a direct signal to 
cancel the leakages. In addition to a reduction in receiver sensitivity, transmitter noise 
can cause erroneous range information. 

The sideband superheterodyne receiver, although more complex than the homodyne 
(zero-IF) receiver, is more sensitive and stable and is preferred wherever its slightly 
more complex construction can be accepted. A block diagram of an FM-CW radar 
with a sideband superheterodyne receiver is shown in Fig. 3ll4. A portion of the 
frequency-modulated transmitter signal is applied to a mixer along with the oscillator 
signal. The selection of the local-oscillator frequency is a bit different from that in the 
usual superheterodyne receiver. The local-oscillator frequency / IF should be the same 
as the intermediate frequency used in the receiver, whereas in the conventional super- 
heterodyne the LO frequency is of the same order of magnitude as the RF signal. The 



\ /&(/) 




•M 










Timing signal 




) 


transmitter 










f (t) 

■ 








1 

1 






Mixer 


fir 


Local 
oscillator 




1 










1 






\ 


f Q U 

<f (t 


) 
>->if 








1 

1 

4 






Sideband 
filter 






Switched 

frequency 

counter 


Doppler 
vejocity 








' 


foit) 


-fir 












' 


A 








' 




\ f U-T) 


Receiver 

mixer 




IF 
amplifier 




Balanced 
detector 




Low-frequency 
amplifier 






J 


flF+f* 




ff 








(f.= fr,{ 


t-D-f n (t 


\\ 








\ 








Average 

frequency 

counter 


Range 



Fig. 3.14. Block diagram of FM-CW radar using sideband superheterodyne receiver. 



output of the mixer consists of the varying transmitter frequency f (t) plus two sideband 
frequencies, one on either side of/ (?) and separated from/ (r) by the local-oscillator 
frequency / IF . The filter selects the lower sideband f (t) — f w and rejects the carrier 
and the upper sideband. The sideband that is passed by the filter is modulated in the 
same fashion as the transmitted signal. The sideband filter must have sufficient 
bandwidth to pass the modulation, but not the carrier or other sideband. The filtered 
sideband serves the function of the local oscillator. 

When an echo signal is present, the output of the receiver mixer is an IF signal of 
frequency / IF +/„, where f b is composed of the range frequency/, and the doppler 
velocity frequency/,. The IF signal is amplified and applied to the balanced detector 
along with the local-oscillator signal/ IF . The output of the detector contains the beat 
frequency (range frequency and the doppler velocity frequency), which is amplified to a 
level where it can actuate the frequency-measuring circuits. 

In Fig. 3.14, the output of the low-frequency amplifier is divided into two channels: 
one feeds an average-frequency counter to determine range, the other feeds a switched 
frequency counter to determine the doppler velocity (assuming f r > f d ). Only the 
averaging frequency counter need be used in an altimeter application, since the rate of 
change of altitude is usually small. 



Sec. 3.3] 



CW and Frequency-modulated Radar 93 



Another example of the superheterodyne principle applied to the FM-CW radar 
receiver is shown in the block diagram of Fig. 3.15. This is known as the signal- 
following superheterodyne. Its principle of operation is quite similar to that of auto- 
matic frequency control (AFC) in a conventional superheterodyne receiver. A 
portion of the transmitter signal is applied to a mixer, along with a portion of the 
local-oscillator signal. The local oscillator may be a reflex klystron or some other 
oscillator whose frequency can be controlled electronically. This local oscillator is 
more like that of a conventional superheterodyne receiver than the oscillator of the 
sideband superheterodyne of Fig. 3.14. Its frequency is the carrier frequency ± the IF 
The difference frequency from the mixer is equal to the IF. The mixer output is 
amplified and applied to a frequency discriminator which generates a d-c voltage 
proportional to the difference between the transmitted and the local-oscillator fre- 
quencies. The discriminator voltage is used to correct the local-oscillator frequency so 
as to vary it in synchronism with the transmitted frequency. The local-oscillator signal 
is applied to the receiver mixer to produce the IF signal. This is amplified and detected 
in the balanced mixer, and its frequency measured. 



^ c 


FM 




- Modulator 






y 


transmitter 








1 


l 
















Mixer 




IF 
amplifier 






IF 
amplifier 








































Local 
oscillator 




D-c 
amplifier 




Frequency 
discriminator 


















> 


1 














1 












I s ! , 


Receiver 




IF 
amplifier 




Balanced 
detector 




Low-frequency 




Frequency 
counter(s) 





mi 


er 










a 


mplifi 


er 





Fig. 3.15. Block diagram of FM-CW radar with signal-following superheterodyne receiver. 



In essence, the local oscillator is made to stay in step with the changing transmitted 
signal in order to provide the proper reference signal at the receiver. However, there 
will always be some lag in the local-oscillator frequency since there must be a difference 
between it and the transmitter if an error is to be discerned. This lag is not important 
since the two IF signals are combined in the balanced detector and are subject to the 
same error. In both the signal-following superheterodyne and the sideband super- 
heterodyne, the RF bandwidth necessary for precise range measurement is discarded 
after its purpose has been served, thus permitting relatively narrow IF bandwidths. 

A target at short range will generally result in a strong signal at low frequency, while 
one at long range will result in a weak signal at high frequency. Therefore the fre- 
quency characteristic of the low-frequency amplifier in the FM-CW radar may be 
shaped to provide attenuation at the low frequencies corresponding to short ranges and 
large echo signals. Less attenuation is applied to the higher frequencies, where the echo 
signals are weaker. 

The echo signal from an isolated target varies inversely as the fourth power of the 
range, as is well known from the radar equation. With this as a criterion, the gain of 
the low-frequency amplifier should be made to increase at the rate of 12 db/octave. 
The output of the amplifier would then be independent of the range, for constant target 
cross section. Amplifier response shaping is similar in function to sensitivity time 
control (STC) employed in conventional pulse radar (Sec. 8.2). However, in the 



94 



Introduction to Radar Systems 



[Sec. 3.3 



altimeter, the echo signal from an extended target such as the ground varies inversely as 
the square (rather than the fourth power) of the range, since the greater the range, the 
greater the echo area illuminated by the beam (Sec. 12.3). For extended targets, 
therefore, the low-frequency amplifier gain should increase 6 db/octave. A com- 
promise between the isolated (12-db slope) and extended (6-db slope) target echoes 
might be a characteristic with a. slope of 9 db/octave. The constant output produced 
by shaping the doppler-amplifier frequency-response characteristic is not only helpful 
in lowering the dynamic range requirements of the frequency-measuring device, but the 
attenuation of the low frequencies effects a reduction of low-frequency interfering noise. 
A typical frequency-response characteristic with a slope of approximately 8 db/octave 
is shown in Fig. 3.16. Lowered gain at low altitudes also helps to reduce interference 
from unwanted reflections. The response at the upper end of the frequency charac- 
teristic is rapidly reduced for frequencies beyond that corresponding to maximum 
range. If there is a minimum target range, the response is also cut off at the low- 
frequency end, to further reduce the extraneous noise entering the receiver. 





6 

12 

a 
» 18 

y% 

c 
o 

£ 

30 

35 

42 
0.1 




0.2 0.3 0.5 0.8 1.0 2 3 5 
Frequency, kc 



8 10 20 30 
Fig. 3.16. Frequency-response characteristic of low-frequency amplifier of typical altimeter. 



Another method of processing the range or height information from an altimeter so 
as to reduce the noise output from the receiver and improve the sensitivity uses a narrow- 
bandwidth low-frequency amplifier with a feedback loop to maintain the beat frequency 
constant. 23 - 25 When a fixed-frequency excursion (or deviation) is used, as in the usual 
altimeter, the beat frequency can vary over a considerable range of values. The 
low-frequency-amplifier bandwidth must be sufficiently wide to encompass the expected 
range of beat frequencies. Since the bandwidth is broader than need be to pass the 
signal energy, the signal-to-noise ratio is reduced and the receiver sensitivity degraded. 
The system shown in the block diagram of Fig. 3 . 1 7 overcomes this limitation. Instead 
of maintaining the frequency excursion A/ constant and obtaining a varying beat 
frequency, A/is varied to maintain the beat frequency constant. The beat-frequency 
amplifier need only be wide enough to pass the received signal energy, thus reducing the 
amount of noise with which the signal must compete. The frequency excursion is 
maintained by a servomechanism to that value which permits the beat frequency to fall 
within the passband of the narrow filter. The value of the frequency excursion is then a 
measure of the altitude and may be substituted into Eq. (3.18). A similar servo- 
mechanism technique may be used to maintain the aircraft at a fixed preset distance 
from the ground. 

When used in the FM altimeter, the technique of servo-controlling the frequency 
excursion is usually applied at all altitudes above a predetermined minimum. Since 
the frequency excursion A/is inversely proportional to range, the radar is better operated 



Sec. 3.3] 



CW and Frequency-modulated Radar 95 



at very low altitudes in the more normal manner with a fixed A/, and hence a varying 
beat frequency. 

The AN/APN-22 radar altimeter is operated in the conventional manner for altitudes 
from to 200 ft. Above 200 ft the frequency excursion is made to vary inversely with 
altitude so as to maintain a constant beat frequency of approximately 6,000 cps. 
Below 200 ft the output of the frequency counter is a measure of range. Above 200 ft 
the output of the potentiometer connected to the servomotor determines the range. 

Another technique that could be used to narrow the bandwidth beat-frequency 
amplifier without the need for a servomechanism is to employ discrete rather than 
continuous frequency excursions. The beat-frequency amplifier would have to be 
designed so that its bandwidth could be changed in discrete steps corresponding to the 
frequency excursion employed. 

The widely used cycle-counting type of frequency meter is simple, stable, and 
accurate. 20 - 21 ' 26 The principle of operation of a frequency counter is based upon 
generating a fixed amount of charge for every cycle or half cycle of the unknown 
frequency. The total charge per second (current) is indicated on a milliammeter 
calibrated in range or altitude. 



* 



FM 
transmitter 



Modulator 



Servomotor 

and 
potentiometer 



Servo 
omplifier 



Balanced 
detector 



Low-trequency 

amplifier 
(narrowband) 



Limiter 



Frequency 
counter 



Height 
indicator 



Fig. 3.17. FM altimeter with servo control of transmitter frequency excursion. 



Measurement Errors. The absolute accuracy of radar altimeters is usually of more 
importance at low altitudes than at high altitudes . Errors of 1 or 20 ft might not be of 
significance when cruising at altitudes of 30,000 ft, but are important if the altimeter is 
part of a blind landing system. 

The theoretical accuracy with which distance can be measured depends upon the 
bandwidth of the transmitted signal and the ratio of signal energy to noise energy. In 
addition, measurement accuracy might be limited by such practical restrictions as the 
accuracy of the frequency-measuring device, the residual path-length error caused by 
the circuits and transmission lines, errors caused by multiple reflections and transmitter 
leakage, and the frequency error due to the turn-around of the frequency modulation. 

As has been mentioned, a common form of frequency-measuring device is the cycle 
counter, which measures the number of cycles or half cycles of the beat during the 
modulation period. The total cycle count is a discrete number since the counter is 
unable to measure fractions of a cycle. The discreteness of the frequency measurement 
gives rise to an error called tht fixed error, or step error. The average number of cycles 
N of the beat frequency f b in one period of the modulation cycle/ m is/Jf m , where the bar 
over/,, denotes time average. Equation (3.18) may be rewritten as 

cN 

4 A/ 
where R = range (altitude), m 

c = velocity of propagation, m/sec 
A/ = frequency excursion, cps 



96 



Introduction to Radar Systems 



[Sec. 3.3 



Since the output of the frequency counter N is an integer, the range will be an integral 
multiple of r/(4 A/) and will give rise to a quantization error equal to 

6R = -£- (3.28a) 

4 A/ 

or a*(ft ) = ^L (3.286) 

A/(Mc) 

Note that the fixed error is independent of the range and carrier frequency and is a 
function of the frequency excursion only. Large frequency excursions are necessary if 
the fixed error is to be small. 

The frequency excursion of the AN/APN-22 altimeter is 70 Mc for altitudes less than 
200 ft. The fixed error is 3.5 ft. If the frequency excursion were one-tenth this value 




2 8/? 38/? 

Range 



4 8/? 



5 8/? 



Fig. 3.18. Variation of beat-frequency cycle count with phase, (a) 5.4 cycles of beat frequency; 
(6) same as (a) but shifted in phase by -n radians; (c) variation of counts with range. 

(7 Mc), the error would be 35 ft, a relatively large error at low altitudes. It will be 
recalled that above 200 ft the frequency excursion is made to vary inversely with 
altitude in the AN/APN-22 by a servomechanism control system. Under these 
conditions (that is, A/ a function of altitude), the fixed error is a function of the 
altitude. However, the fixed error expressed as a percentage will be constant. 

The count measured by a frequency counter depends upon the phase of the beat 
frequency with respect to the time interval over which the measurement is made. In 
addition, the count will depend on the particular configuration of the counter, that is, 
whether it counts threshold crossings or zero crossings or whether it is full wave (2 
counts per cycle) or half wave (1 count per cycle). The dependence on the phase of 
the beat frequency may be illustrated by considering a counter which counts only those 
zero crossings with positive slope (1 count per cycle). Assume that the beat-frequency 
signal is 5.4 cycles in duration over the modulation period. If the phase relative to the 
modulation period were like that shown in Fig. 3. 1 8a, the count of positive zero crossings 
would be 5, but if the phase were shifted tt radians, the count would be 6 ; another shift 
of v radians would change the count back to 5. The phase of the beat-frequency 
signal, according to Eq. (3.22), will change by v radians \f2nf T = AttR\X changes by n 
radians ; this corresponds to a change in range of one-quarter of a wavelength. At 
radar frequencies, a quarter wavelength is small compared with the fixed range error 



Sec. 3.3] CW and Frequency-modulated Radar 97 

dR caused by the discrete measurement of frequency. Therefore the fixed error will 
jump back and forth between N and N + 1 cycles every time the range changes by 
one-quarter of a wavelength. If a full- wave counter were used, the count would jump 
back and forth every eighth wavelength. The uncertainty in the count N is illustrated in 
Fig. 3.18c. The units of range are in increments of fixed error dR = c/(4 A/). Every 
time the phase of the echo signal changes by w radians (or njl radians for a full-wave 
counter), the count increases or decreases by 1. The count also changes by 1 every 
time the range changes by dR. For example, if the frequency meter reads a count of 3, 
the range uncertainty would lie between 2SR and 4dR. 

At high altitudes, the inaccuracy caused by the fixed error is usually of little or no 
operational importance unless A/is small. Normal fluctuations in aircraft altitude due 
to uneven terrain, waves on the water, or turbulent air average out the fixed error 
provided the time constant of the indicating device is large compared with the time 
between fluctuations. Over smooth terrain such as airport runways or calm water, the 
fixed error might not be averaged out and could prove troublesome. 

There are several techniques that can be used to make the fixed error small, if there is 
reason to do so. One technique, already mentioned, is to make the frequency excursion 
A/ large. Most altimeters are designed with excursions of the order of 100 Mc, 
resulting in a fixed error of a few feet. The effects of the fixed error also can be reduced 
by wobbling the modulation frequency or the phase of the transmitter output. Wob- 
bling the transmitter phase results in a wobbling of the phase of the beat signal. An 
average reading between N and N + 1 will be obtained when displayed on a normal 
meter movement. The AN/APN-22 employs the technique of varying the modulation 
frequency at a 10-cps rate, causing the phase shift of the beat signal to vary. The 
indicating system is designed so that it does not respond to the 10-cps modulation 
directly, but it averages the fixed error in a manner similar to the averaging accomplished 
by changes in altitude. 

Another method which has been employed to average the fixed error is to vary the 
phase of the reference signal / ref by transposing to a frequency / ref +/ t , where f x is a 
frequency small compared with the modulation frequency / m . 27 The phase shift 
associated with the beat signal will be 2irf T [from Eq. (3.22)] plus 2-nfy. The total 
phase shift therefore varies with time and permits the fixed error to be averaged. 

The above methods assume that the radar application permits sufficient time for the 
averaging to take place. In the FM altimeter this condition is usually satisfied. In 
other applications of FM-CW radar, such as a scanning search radar, the necessity of 
averaging over an interval of time may increase the scan rate and prove to be an 
unacceptable restriction. 

The fixed error is not present in a noncounting (continuous) frequency meter such as 
a frequency discriminator. The discriminator output is a voltage proportional to 
frequency and is continuous rather than discrete. However, discriminator circuits 
with sufficient stability and linearity do not seem to be capable of as wide a range of 
frequency operation as the frequency counter and in the past have not been popular in 
FM altimeter systems. Also, when both range and doppler information are required, 
the discriminator circuit is more difficult to operate as a switched frequency meter than 
is the counter. The restriction caused by the limited bandwidth of the frequency 
discriminator may be overcome by transposing the relatively low beat frequency to a 
higher frequency in an effort to reduce the required percentage bandwidth. The 
discriminator might be used in those altimeters mentioned previously where the 
frequency deviation is controlled by a servomechanism which maintains the beat 
frequency constant. 

A different method of employing a frequency discriminator to obtain both the range 
and doppler velocity is shown in Fig. 3.19. This technique not only eliminates the fixed 



98 



Introduction to Radar Systems 



[Sec. 3.3 

error, but it does not confuse the range and doppler velocity of fast, nearby targets 
(when/i >f r ) as does the combination of average and switched frequency counters. 28 
The system as described in Ref. 28 actually employs a triple-conversion receiver rather 
than the single-conversion receiver shown. There is no loss in generality in considering 
the simpler system. Basically, the system up to the input of the limiter is quite similar 
to the sideband superheterodyne receiver discussed previously (Fig. 3.14). The 
voltage from the IF amplifier preceding the limiter is 
vn, = k sin [2-rrf lv (t + T) ± 2nf d t + nAfTcos (2nf m t - 4> T ) + </>] = k sin O (3.29) 

where/ IF is the frequency of the IF;f d , the doppler frequency; <f> represents the various 
constant phase shifts introduced in the system; <j> T = irf m T, T = 2R/c; and the other 



FM 
transmitter 



Modulator 



Mixer *■ 



Local 



Sideband 
filter 



»" 



Direct-current 
output proportional 
to Doppler velocity 



Mixer 



IF 
amplifier 



Limiter 



Frequency 
discriminator 



Selective 
amplifier at 
frequency-^ 



Amplitude of 
output at 
-frequency f m 
corresponds 
to range 



Fig. 3.19. Block diagram of FM-CW technique for eliminating the fixed error. 



parameters are as denned in Eq. (3.22). Differentiating O to obtain the frequency of 
the signal leaving the IF amplifier gives 

27rA# m K 



Ja ~2ndt~ Jw±Jd 



•sin(27r/ m t- <f> T ) 



(3.30) 



If this frequency is applied to a frequency discriminator centered at the intermediate 
frequency / IF , the output voltage will consist of a steady component corresponding to 
the doppler frequency f d and an a-c component of frequency f m with amplitude pro- 
portional to range. Therefore the doppler velocity may be measured by averaging the 
discriminator output. Range may be determined by extracting the a-c component in a 
narrowband filter centered about the frequency f m and calibrating the output voltage 
from this filter directly in range. The doppler velocity and the range must not vary 
appreciably over the averaging period if accurate measurements are to be obtained. 

Another technique for eliminating the fixed error is known as the double-modulated 
FM radar. 20 ' 29 In this system (Fig. 3.20) the transmitted signal is modulated at two 
frequencies/*.! and/ m2 . The modulating frequency f ml is of low frequency and corre- 
sponds to the modulating frequency (/J in the usual FM system, while/ m2 is a relatively 
high frequency (f m2 >/ ml ). The frequency f ml might be of the order of 100 cycles, 
while f mi might be a few kilocycles. The received signal is mixed with the reference 
signal, and an IF signal is extracted whose frequency is some multiple (including unity) 
of/ m2 ± the doppler frequency f d . Therefore, if this signal is amplified, limited, and 
applied to a frequency discriminator, its output will contain two components, just as in 
the system described in Fig. 3.19. One component is d-c, which is proportional to the 
doppler frequency shift (±f d ), and hence to target relative velocity. The other is the 
a-c component at a frequency f ml whose amplitude is proportional to target range. 
The double FM system eliminates the fixed error and permits a smaller frequency 
deviation to be used than in the usual FM system. However, it is more complicated 



Sec. 3.3] 



CW and Frequency-modulated Radar 99 



than the system of Fig. 3.19 and is more limited in both maximum range and minimum 
range than either the previous system or the usual FM system. 

Before leaving the subject of fixed error, it may be worthwhile to mention briefly the 
relation between transmitted bandwidth and accuracy. In Chap. 10, the factors which 
affect the accuracy of radar measurements are discussed, and it is mentioned that the 
accuracy with which range can -be measured is a function of the transmitted spectral 
width, the signal-to-noise ratio, and the number of independent observations. The 
wider the transmitted spectrum and the greater the signal-to-noise ratio, the more 
accurate will be the range measurement. Those FM systems such as described by 
Figs. 3.19 and 3.20 whose frequency excursions are only a fraction of that of the usual 



± 



FM 
transmitter 



Modulator f m1 



,»f m 



Modulator f mZ 



Mixer 



H- 



90° 
phase 
shift 



Bandposs 
filter 



90° 
phase 
shift 



Direct-current 
output proportional 
to doppler velocity 



-»| Mixer | «- 



Bandposs 
filter 



IF 
amplifier 



and limiter 



Frequency 
discriminator 



Amplifier 



Amplitude of 
output at 
■frequency f m 
corresponds 
to range 



Fig. 3.20. Block diagram of double-modulated FM radar. 

FM radar system must take more time or make more observations or obtain higher 
signal-to-noise ratios if comparable accuracy is to be achieved. 

Other errors might be introduced in the CW radar if there are uncontrolled variations 
in the transmitter frequency, modulation frequency, or frequency excursion. Target 
motion can cause an error in range equal to v r T , where v r is the relative velocity and T 
is the observation time. At short ranges the residual path error can also result in a 
significant error unless compensated for. The residual path error is the error caused 
by delays in the circuitry and transmission lines. Multipath signals also produce 
error. Figure 3.21 shows some of the unwanted signals that might occur in the FM 
altimeter. 22 The wanted signal is shown by the solid line, while the unwanted signals 
are shown by the broken arrows. The unwanted signals include : 

1. The reflection of the transmitted signals at the antenna caused by impedance 
mismatch. 

2. The standing-wave pattern on the cable feeding the reference signal to the receiver, 
due to poor mixer match. 

3. The leakage signal entering the receiver via coupling between transmitter and 
receiver antennas. This can limit the ultimate receiver sensitivity, especially at high 
altitudes. 

4. The interference due to power being reflected back to the transmitter, causing a 
change in the impedance seen by the transmitter. This is usually important only at low 
altitudes. It can be reduced by an attenuator introduced in the transmission line at 
low altitude or by a directional coupler or an isolator. 

5. The double-bounce signal. 

Multipath reflections (reflections from unwanted targets) can also introduce errors 
into the FM-CW radar system and must be avoided. 30 They can be reduced with 



100 



Introduction to Radar Systems 



[Sec. 3.3 



Transmitter 



f 



t© 



© 



Receiver 



highly directive antennas and in ground-based radars by lowering the height of the 
antenna to reduce the path difference between the direct and the reflected rays. These 
remedies only relieve rather than eliminate completely the problem of multipath. 

Transmitter Leakage. The sensitivity of FM-CW radar is limited by the noise 
accompanying the transmitter signal which leaks into the receiver. Although advances 
have been made in reducing the AM and FM noise generated by high-power CW 
transmitters, the noise is usually of sufficient magnitude compared with the echo signal 
to require some means of minimizing the leakage that finds it way into the receiver. 

The techniques described previously for reduc- 
ing leakage in the CW radar apply equally 
well to the FM-CW radar. Separate antennas 
and direct cancellation of the leakage signal 
are two techniques which give considerable 
isolation. 

The degree of isolation that can be obtained 
by cancellation of the leakage signal might 
vary from 10 db 9 to 60 db, 31 depending on the 
method employed for adjusting and maintain- 
ing the phase and amplitude of the cancellation 
signal to the correct values. To obtain a can- 
cellation of as much as 60 db (residual voltage 
one-thousandth the original) requires a closed- 
loop servo system to automatically correct for 
changes in the leakage signal produced by 
antenna scanning and the like. 

The double-sideband noise components of 

the transmitter may be further canceled in the 

CW radar receiver with a simple AM cancellation network. 31 The received signal is 

not affected by a double-sideband cancellation network since a doppler-frequency- 

shifted signal is equivalent to a single-sideband modulation. 

The ability of the FM-CW radar to measure range provides an additional basis for 
obtaining isolation. Echoes from short-range targets— including the leakage signal- 
may be attenuated relative to the desired target echo from longer ranges by properly 
processing the difference-frequency signal obtained by heterodyning the transmitted 
and received signals. 

If the CW carrier is frequency-modulated by a sine wave, the difference frequency 
obtained by heterodyning the returned signal with a portion of the transmitter signal 
may be expanded in a trigonometric series whose terms are the harmonics of the 
modulating frequency f m . 8 ' 20 Assume the form of the transmitted signal to be 




ind 



Fig. 3.21. Unwanted signals in FM altim- 
eter. (From Capelli, 22 IRE Trans.) 



sin 



\2irf t + ^f sin 2nf a 



2f„, 



•) 



(3.31) 



where f = carrier frequency 

f m = modulation frequency 

A/= frequency excursion (equal to twice the frequency deviation) 
The difference frequency signal may be written 

»d = UD) cos (Infy - 4> Q ) + 2J 1 {D) sin (2irf d t - <f> ) cos (2nf m t - <f>J 

- 2J 2 (D) cos (2nf d t - fa) cos 2(27rf m t - <f>J 

- 2J 3 (D) sin (27rf d t - fa) cos 3(2nf m t - <£J 

+ 2/ 4 (Z>) cos {2irf a t - fa) cos 4 (2nf m t - <t> m ) + 2/ 5 (£>) • • • (3.32) 



Se c 3.3] CW and Frequency-modulated Radar 101 

where J , J x , J 2 , etc. = Bessel functions of first kind and order 0, 1 , 2, etc., respectively 
D = (Af If J sin 2nf m R /c 

R = distance to target at time t = (distance that would have been 
measured if target were stationary) 
c = velocity of propagation 
fa = 2v r f /c = doppler frequency shift 
v r = relative velocity of target with respect to radar 
<f> = phase shift approximately equal to angular distance 4Trf R jc 
<f> m = phase shift approximately equal to 2-nf m R^c 
The difference-frequency signal of Eq. (3.32) consists of a doppler-frequency com- 
ponent of amplitude J (D) and a series of cosine waves of frequency f m , 2f m , 3f m , etc. 
Each of these harmonics of f m is modulated by a doppler-frequency component with 
amplitude proportional to J„(D). The product of the doppler-frequency factor times 
the nth harmonic factor is equivalent to a suppressed-carrier double-sideband modula- 
tion (Fig. 3.22). 



34, 



4/S» 



fm 2'm 

Frequency 

Fig. 3.22. Spectrum of the difference-frequency signal obtained from an FM-CW radar sinusoidally 
modulated at a frequency/™ when the target motion produces a doppler frequency shift L. (After 
Saunders* IRE Trans.) J J 

In principle, any of the /„ components of the difference-frequency signal can be 
extracted in the FM-CW radar. Consider first the d-c term J (D) cos (2nf d t - <£ ). 
This is a cosine wave at the doppler frequency with an amplitude proportional to J (D). 
Figure 3.23 shows a plot of several of the Bessel functions. The argument D of the 
Bessel function is proportional to range. The J amplitude applies maximum response 
to signals at zero range in a radar that extracts the d-c doppler-frequency component. 
This is the range at which the leakage signal and its noise components (including 
microphony and vibration) are found. At greater ranges, where the target is expected, 
the effect of the J Bessel function is to reduce the echo-signal amplitude in comparison 
with the echo at zero range (in addition to the normal range attenuation). Therefore, 
if the J term were used, it would enhance the leakage signal and reduce the target signal, 
a condition opposite to that desired. 

An examination of the Bessel functions (Fig. 3.23) shows that if one of the modulation- 
frequency harmonics is extracted (such as the first, second, or third harmonic), the 
amplitude of the leakage signal at zero range may theoretically be made equal to zero. 
The higher the number of the harmonic, the higher will be the order of the Bessel 
function and the less will be the amount of microphonism-leakage feed through. This 
results from the property that J n (x) behaves as x n for small x. Although higher-order 
Bessel functions may reduce the zero-range response, they may also reduce the response 
at the desired target range if the target happens to fall at or near a range corresponding 
to a zero of the Bessel function. When only a single target is involved, the frequency 
excursion A/can be adjusted to obtain that value of D which places the maximum of the 
Bessel function at the target range. 



102 Introduction to Radar Systems [Sec. 3.3 

The technique of using higher-order Bessel functions has been applied to the type of 
doppler-navigation radar discussed in the next section. A block diagram of a CW 
radar using the third harmonic (/ 3 term) is shown in Fig. 3.24. The transmitter is 
sinusoidally frequency-modulated at a frequency f m to generate the waveform given by 



-J {D) 




12 D 



-0.4 



Fig. 3.23. Plot of Bessel functions of order 0, 1 , 2, and 3 ; D = (A///J sin 2irf m Rt,lc. 

Eq. (3.31). The doppler-shifted echo is heterodyned with the transmitted signal to 
produce the beat-frequency signal of Eq. (3.32). One of the harmonics of/ m is selected 
(in this case the third) by a filter centered at the harmonic. The filter bandwidth is wide 
enough to pass both doppler-frequency sidebands. The filter output is mixed with the 
(third) harmonic of/ OT . The doppler frequency is extracted by the low-pass filter. 

Circulator Directional 
^\ coupler 



^> 



Transmitter 



f m Frequency 
modulation 



x3 
frequency 
multiplier 



Mixer 



3d harmonic 
filter 



Mixer 



Low-pass 
filter 



Doppler 
frequency 



Fig. 3.24. Sinusoidally modulated FM-CW radar extracting the third harmonic {J z Bessel com- 
ponent). 

Since the total energy contained in the beat-frequency signal is distributed among all 
the harmonics, extracting but one component wastes signal energy contained in the 
other harmonics and results in a loss of signal as compared with an ideal CW radar. 
However, the signal-to-noise ratio is generally superior in the FM radar designed to 
operate with the nth harmonic as compared with a practical CW radar because the 
transmitter leakage noise is suppressed by the nth-order Bessel function. The loss in 
signal energy when operating with the J 3 Bessel component is reported 839 to be from 4 



Sec. 3.4] CW and Frequency-modulated Radar 103 

to 10 db. Although two separate transmitting and receiving antennas may be used, it 
is not necessary in many applications. A single antenna with a circulator is shown in 
the block diagram of Fig. 3.24. Leakage introduced by the circulator and by reflections 
from the antenna are at close range and thus are attenuated by the J z factor. 

A plot of J 3 (D) as a function of distance is shown in Fig. 3.25. The curve is mirrored 
because of the periodicity of D. The nulls in the curve suggest that echoes from 
certain ranges can be suppressed if the modulation parameters are properly selected. 

If the target is stationary (zero doppler frequency), the amplitudes of the modulation- 
frequency harmonics are proportional to J n {D) sin </> or J n (D) cos <f> , where 
<f> = Att^RqIc = AttRqIL Therefore the amplitude depends on the range to the 
target in RF wavelengths. The sine or the cosine terms can take any value between 
+ 1 and — 1, including zero, for a change in range corresponding to one RF wavelength. 
For this reason, the extraction of the higher-order modulation frequencies is not 
practical with a stationary target, such as in an altimeter. 

In order to use the properties of the Bessel function to obtain isolation in an FM-CW 




Distance 
Fig. 3.25. Plot of / 3 (Z>) as a function of distance. {From Saunders* IRE Trans.) 

altimeter, when the doppler frequency is essentially zero, the role of the doppler fre- 
quency shift may be artificially introduced by translating the reference frequency to 
some different value. This might be accomplished with a single-sideband generator 
(frequency translator) inserted between the directional coupler and the RF mixer of 
Fig. 3.24. The frequency translation in the reference signal path is equivalent to a 
doppler shift in the antenna path. The frequency excursion of the modulation wave- 
form can be adjusted by a servomechanism to maintain the maximum of the Bessel 
function at the aircraft's altitude. The frequency translator is not needed in an airborne 
doppler navigator since the antenna beam is directed at a depression angle other than 
90° and a doppler-shifted echo is produced by the motion of the aircraft. 

3.4. Airborne Doppler Navigation 3240 

An important requirement of aircraft flight is for a self-contained navigation system 
capable of operating anywhere over the surface of the earth under any conditions of 
visibility or weather. It should provide the necessary data for piloting the aircraft from 
one position to another without the need of navigation information transmitted to the 
aircraft from a ground station. One method of obtaining a self-contained aircraft 
navigation system is based on the CW doppler-radar principle. Doppler radar can 
provide the drift angle and true speed of the aircraft relative to the earth. The drift 
angle is the angle between the horizontal projection of the centerline of the aircraft 
(heading) and the horizontal component of the aircraft velocity vector (ground track). 
From the ground-speed and drift-angle measurements, the aircraft's present position 
can be computed by dead reckoning. 

An aircraft with a doppler radar whose antenna beam is directed at an angle y to the 
horizontal (Fig. 3.26a) will receive a doppler-shifted echo signal from the ground. The 
shift in frequency is/ d = (fjc) v cos y, where/ is the carrier frequency, v is the aircraft 
velocity, and c is the velocity of propagation. Typically, the depression angle y might 
be in the vicinity of 65 to 70°. A single antenna beam from a doppler radar measures 



104 Introduction to Radar Systems [Sec. 3.4 

one component of aircraft velocity relative to the direction of propagation. A mini- 
mum of three noncoplanar beams are needed to determine the vector velocity, that is, 
the speed and direction of travel. 

Doppler-navigation radar measures the vector velocity relative to the frame of 
reference of the antenna assembly. To convert this vector velocity to a horizontal 
reference on the ground, the direction of the vertical must be determined by some 
auxiliary means. The heading of the aircraft, as might be obtained from a compass, 



A=*- 



(/>) 



Fig. 3.26 (a) Aircraft with single doppler-navigation antenna beam at an angle y to the horizontal; 
(0) aircraft employing four doppler-navigation beams to obtain vector velocity. 

must also be known for proper navigation. The vertical reference may be used either 
to stabilize the antenna beam system so as to align it with the horizontal, or alternatively, 
the antennas might be fixed relative to the aircraft and the ground velocity components 
calculated with a computer. 

A practical form of doppler-navigation radar might have four beams oriented as in 
Fig. 3.266. A doppler-navigation radar with forward and rearward beams is called a 
Janus system, after the Roman god who looked both forward and backward at the same 
time. Assume initially that the two forward and two backward beams are symmetri- 
cally disposed about the axis of the aircraft. If the aircraft's velocity vector is not in 
the same direction as the aircraft heading, the doppler frequency in the two forward 
beams will not be the same. This difference in frequency may be used to generate an 
error signal in a servomechanism which rotates the antennas until the doppler fre- 
quencies are equal, indicating that the axis of the antennas is aligned with the ground 
track of the aircraft. The angular displacement of the antenna from the aircraft 



Sec. 3.4] CW and Frequency-modulated Radar 105 

heading is the drift angle, and the magnitude of the doppler is a measure of the speed 
along the ground track. 

The use of the two rearward beams in conjunction with the two forward beams 
results in considerable improvement in accuracy. It eliminates the error introduced by 
vertical motion of the aircraft and reduces the error caused by pitching movements of 
the antenna. 

Navigation may also be performed with only two antenna beams if some auxiliary 
means is used to obtain a third coordinate. Two beams give the two components of 
the aircraft velocity tangent to the surface of the earth. A third component, the vertical 
velocity, is needed and may be provided from some nondoppler source such as a 
barometric rate-of-climb meter. The primary advantage of the two-beam system is a 
reduction in equipment. However, the accuracy is not as good as with systems using 
three or four beams. 

In principle, the CW radar would seem to be the ideal method of obtaining doppler- 
navigation information. However, in practice, the CW radar is not adequate at long 
ranges. Leakage between transmitter and receiver limits the sensitivity of the CW 
doppler-navigation radar, j ust as it does in any C W radar. One method of eliminating 
the ill effects of leakage is by pulsing the transmitter on and turning the receiver off for 
the duration of the transmitted pulse in a manner similar to the pulse-doppler radar 
described in Sec. 4.5. The pulse-doppler mode of operation has the further advantage 
in that each beam can operate with a single antenna for both transmitter and receiver, 
whereas a CW radar must usually employ two separate antennas in order to achieve the 
needed isolation. However, pulse systems suffer from loss of coverage and/or sensi- 
tivity because of "altitude holes." These are caused by the high prf commonly used with 
pulse-doppler radars when it is necessary to achieve unambiguous doppler measure- 
ments. The high prf, although it gives unambiguous doppler, usually results in 
ambiguous range. But more important, a pulse radar with ambiguous prf can result in 
lost targets. If the transmitter is pulsed just when the ground echo arrives back at the 
radar, it will not be detected. Thus, altitude holes exist at or near those altitudes where 
the echo time is an integral multiple of the pulse-repetition period. Techniques exist 
for reducing the undesired effects of altitude holes, but not without some inconvenience 
or possible loss in over-all performance. 33 

The pulse-doppler system must be coherent from pulse to pulse if the doppler 
frequency shift is to be correctly measured. A transmitted signal might be obtained 
with a low-power CW oscillator followed by an amplifier that is pulsed on and off at the 
desired rate. In essence, a pulse-doppler radar may be considered as a "sampled CW" 
radar. 

The Janus system can be operated incoherently by using the same transmitter to feed 
a pair of beams simultaneously. Typically, one beam is directed ahead and to the right 
of the ground track, and the other aft and to the left. A forward-left and an aft-right 
are also fed by the transmitter as a second channel. The two channels may be operated 
simultaneously or timed-shared. By heterodyning in a mixing element the echo signal 
received in the fore and aft beams, the doppler frequency is extracted. The difference 
frequency resulting from the mixing operation is twice the doppler frequency. A 
stable transmitter frequency is not needed in this system as it is in the coherent system. 
Coherence is obtained on a relative basis in the process of comparing the signals 
received from the forward and backward direction. Changes in transmitter frequency 
affect the echo signals in the two directions equally and are therefore canceled when 
taking the difference frequency. 

Another method of achieving the necessary isolation in a doppler-navigation radar 
is with a frequency-modulated CW system. By frequency-modulating the trans- 
mission, the leakage signal may be reduced relative to the signal from the ground by 



106 Introduction To Radar Systems 



[Sec. 3.5 



extracting a harmonic of the modulating frequency and taking advantage of one of the 
higher-order Bessel functions as described in the previous section. It has been claimed 
that a doppler-navigation system based on this principle can provide 1 50 db of isolation, 
the amount necessary to operate at altitudes of 50,000 ft. 38 

At altitudes of 40,000 ft the doppler navigator can reliably measure distances over 
land to an accuracy of at least 0.5 per cent and drift angles to 0.5°. 38 Over water the 
accuracies are slightly worse. One source of error overSvater is due to an increase in 
specular reflection of the incident beam. Specular reflection reduces the back- 
scattered energy, thus lowering the signal-to-noise ratio. It also causes an apparent 
increase in the angle of depression by favoring the returns from the lower half of the 
incident beam. This results in an error in the ground speed. Another source of error 
is the mass movement of water caused by tides, currents, or winds, which results in a 
doppler frequency shift in addition to that caused by the aircraft's motion. 

3.5. Multiple-frequency CW Radar 942 47 

The radar measurement of time delay or range is fundamentally the measurement of 
the variation of phase with frequency, when time and direction remain constant (Sec. 
10.2). The pulse radar and the FM-CW radar can be analyzed in these terms, but they 

are easier to conceive and understand by analysis in 
the time domain. However, the measurement of 
range with multiple CW frequencies, 5 - 943 to be de- 
scribed in this section, is a direct application of 
the principle that a range measurement is a phase- 
difference measurement. 

Consider the problem of measuring the range R of a 
single stationary target by using a CW radar radiating 
a single-frequency sine wave of the form sin 2nf t. 
(The amplitudes of the signals are all taken to be unity 
since they do not influence the result.) The sine-wave 
signal travels to the target and returns to the radar 
after a time T = 2R/c, where c is the velocity of prop- 
agation. If the transmitted and received signals 
are compared in a phase detector, the output is pro- 
portional to the phase difference between the two 
signals and is A</> = 27rf T = 4Trf R/c. The phase 
difference may therefore be used as a measure of the 
range. 

„ __ c Ac/> _ X 

4Trf 4t7 



KA/-H 



Frequency 
(a) 



£l- 



Frequency 
it) 



-A^ 



(3.33) 



Fig. 3.27. Transmitted (a) and 
received (b) signal spectra in the 
two-frequency CW radar. 



The measurement of the phase difference A</> is 
unambiguous only if A<£ does not exceed 2-n radians. 
(A phase of 2t7ii + A<f> radians, where n is an integer, 
cannot be distinguished from a phase of A</> radians.) Substituting A<f> = 2n into Eq. 
(3.33) gives the maximum unambiguous range as equal to A/2. At radar frequencies 
this unambiguous range is much too small to be of practical interest, although it may 
be quite adequate for certain types of position-finding equipment at relatively low 
frequencies. 

The region of unambiguous range may be extended considerably by transmitting two 
separate CW signals differing only slightly in frequency. 9 It will be shown that the 
measurement of range using two CW frequencies results in an unambiguous range 
which corresponds to a half wavelength at the difference frequency. Consequently, the 



Sec. 3.5] CW and Frequency-modulated Radar 107 

unambiguous range can be made considerably greater than that obtained when only a 
single frequency is transmitted. 

The transmitted waveform is assumed to consist of two continuous sine waves of 
frequency/ and/ 2 (Fig. 3.27a) separated by an amount A/. For convenience, the 
amplitudes of all signals are set equal to unity. The voltage waveforms of the two 
components of the transmitted signal v 1T and v 2T may be written as 

v 1T = sin (2-nfit + <£i) (3.34a) 

v 2T = sin (Infy + fc) (3.34Z>) 

where <^ and <f> 2 are arbitrary (constant) phase angles. The echo signal is shifted in 
frequency by the doppler effect (Fig. 3.27b). The form of the doppler-shifted signals at 
each of the two frequencies/! and/ is similar to Eq. (3.16) and may be written 



v 1R = sin 



v 9J? = sin 



2HA ±/„i)t - ^^ T 2TTf dl t + & 
c 

Mh ±/«)' - ^2 T 2nf d2 t + <f> 2 



(3.35a) 



(3.35b) 



where R = range to target at a particular time t = t (range that would be measured 
if target were not moving) 
f dl = doppler frequency shift associated with frequency/], 
f d2 = doppler frequency shift associated with frequency / 2 

Since the two RF frequencies/ and/ 2 are approximately the same (that is,/ 2 = / + A/ 

where A/ </) the doppler frequency shifts f dl and/ 2 are approximately equal to one 

another. Therefore we may write f dl =f d2 =f d - 
The receiver separates the two components of the echo signal and heterodynes each 

received signal component with the corresponding transmitted waveform and extracts 

the two doppler- frequency components given below: 

v 1B = sin (±27rf a t - ^^ T 2*f d t^ (3.36a) 

v 2D = sin (±2tt// - ^p> T 2-rrf^ (336b) 

The phase difference between these two components is 

^ = Mf 2 - fl )R = Ajr^fR, 
c c 

Hence r = lM- (3 .38) 

4-n-A/ 

which is the same as that of Eq. (3.33), with A/substituted in place of/. 

A block diagram of a two-frequency CW radar is shown in Fig. 3.28. The equipment 
is like that of the simple CW radar except for the addition of the second channel and a 
phase-measuring device. 

The two-frequency CW technique for measuring range was described as using the 
doppler frequency shift. When the doppler frequency is zero, as with a stationary 
target, the method may still be applied by measuring the phase difference between the 
two RF carrier signals. If the target carries a beacon or some other form of echo-signal 
augmentor, the doppler frequency shift may be simulated by translating the echo fre- 
quency, as with a single-sideband modulator. 



108 



Introduction to Radar Systems 



[Sec. 3.5 

If the doppler frequency f d is less than one-half the difference between the two trans- 
mitted frequencies, that is,f d < A//2, the two signals may be readily separated. On the 
other hand, if f d > A//2, each transmitted signal lies within the doppler-frequency 
acceptance band of the other receiver, and unless the transmitted frequencies and their 
harmonics are rejected by the insertion of narrow bandstop niters, they may swamp the 
doppler signals from the target. Since the insertion of rejection niters complicates the 
receiver and eliminates a portion of the doppler-frequency band, it is usually desirable 
to make the difference frequency greater than the expected range of doppler frequencies. 

A large difference in frequency between the two transmitted signals improves the 
accuracy of the range measurement since large A/means a proportionately large change 



Transmitter 



Receiver 




A ^ Range 
indicator 



Fig. 3.28. Block diagram of the two-frequency CW radar for the measurement of range. 

in A<f> for a given range. However, there is a limit to the value of A/, since A<£ cannot be 
greater than 2n radians if the range is to remain unambiguous. The maximum 
unambiguous range .R„ nail ,i> is 



R 



unamb — 



2 A/ 



(3.39) 



Therefore A/ must be less than c/2/? unamb . This relationship is plotted in Fig. 3.29. 
Note that when A/ is replaced by the pulse repetition rate, Eq. (3.39) gives the maximum 
unambiguous range of a pulse radar. 

As an example, consider a two-frequency radar with/i = 3,000 Mc {X = 10 cm). 
If the maximum target velocity is 600 knots, the maximum expected doppler frequency 
is f d = 6,180 cps. Therefore the difference between the two frequencies must be 
greater than 6, 1 80 cps if the difference frequency is to fall outside the passband of the 
doppler filters. The maximum unambiguous range in this case is approximately 13 
nautical miles. 

A qualitative explanation of the operation of the two-frequency radar may be had by 
considering both carrier frequencies to be in phase at zero range. As they progress 
outward from the radar, the relative phase between the two increases because of their 
difference in frequency. This phase difference may be used as a measure of the elapsed 
time. When the two signals slip in phase by 1 cycle, the measurement of phase, and 
hence range, becomes ambiguous. 

The two-frequency CW radar is essentially a single-target radar since only one phase 
difference can be measured at a time. If more than one target is present, the echo signal 
becomes complicated and the meaning of the phase measurement is doubtful. If one 
echo is much stronger than the other, the system might be designed to measure the range 
of this target and ignore the others. 9 In addition to discrimination on the basis of 



Sec. 3.5] 



CW and Frequency-modulated Radar 



109 



amplitude, multiple targets can be discriminated on the basis of doppler. A series of 
narrowband doppler niters can separate signals, or else a single tunable narrowband 
doppler filter may be time-shared over the entire band of doppler frequencies. The 
theoretical accuracy with which range can be measured with the two-frequency CW 
radar can be found from the methods described in Sec. 1 0.5. It can be shown that the 
theoretical rms range error is 



SR = 



4nAf(2EIN f 



(3.40) 



where E = energy contained in received signal 
N = noise power per cycle of bandwidth 
If this is compared with the rms range error theoretically possible with the linear FM 
pulse-compression waveform whose spectrum occupies the same bandwidth A/, the 
error obtained with the two-frequency CW waveform is less by the factor 0.29. 





U,W>J 


_ II 1 1 1! 1 1 1 


II 1 1 1 1 M L 


~ 


7,000 


s. 




o 








T3 








o 


5,000 


\ 


- 




4,000 


^v 


_ 


3 








Q. 


3,000 




— 


£ 
















Q. 


2,000 




- 










O 




— \^ 


— 


(/I 








o 


1,000 


— Nw 


— 


<J 


700 


_ 


^v _ 


o 




— 


\. — 


3 


500 




N. 


a- 


400 




^V 


<x> 


300 




N. - 


c 








a> 










200 
100 


ii ii 


II 1 1 1 1 l\ 1 



10 



20 40 60 80 100 200 400 600 1,000 

Maximum unambiguous range, nautical miles 



Fig. 3.29. Maximum unambiguous range vs. difference frequency in the two-frequency CW radar. 

Equation (3.40) indicates that the greater the separation A/ between the two fre- 
quencies, the less will be the rms error. However, the frequency difference must not be 
too large if unambiguous measurements are to be made. The selection of A/represents 
a compromise between the requirements of accuracy and ambiguity. Substituting the 
unambiguous range of Eq. (3.39) into Eq. (3.40) gives the rms error as 



6R = 



°unam6 

2 7 7(2£/A/ ) i 



(3.41) 



Both accurate and unambiguous range measurements can be made by transmitting 
three or more frequencies instead of just two. For example, if the three frequencies/!, 
/ 2 , and/ 3 are such that/ 3 — f t = k(f 2 — /i), where k is a factor of the order of 1 or 20, 
the pair of frequencies/3,/i gives an ambiguous but accurate range measurement while 
the pair of frequencies/a,/! are chosen close enough to resolve the ambiguities in the/ 3 , 
/j measurement. Likewise, if further accuracy is required, a fourth frequency can be 



110 Introduction to Radar Systems [Sec. 3.5 

transmitted and its ambiguities resolved by the less accurate but unambiguous measure- 
ment obtained from the three frequencies/i,/ 2 ,/ 3 . As more frequencies are added, the 
spectrum and target resolution approach that obtained with a pulse or an FM-CW 
waveform. 

The measurement of range by measuring the phase difference between separated 
frequencies is analogous to the measurement of angle by measuring the phase difference 
between widely spaced antennas, as in an interferometer antenna. The interferometer 
antenna gives an accurate but ambiguous measurement of angle. The ambiguities may 
be resolved by additional antennas spaced closer together. The spacing between the 
individual antennas in the interferometer system corresponds to the separation between 
frequencies in the multiple-frequency distance-measuring technique. The minitrack 
system is an example of an interferometer in which angular ambiguities are resolved in a 
manner similar to that described. 41 

Both the interferometer antenna and the multiple-frequency CW radar are single- 
target devices. If two echo signals are alike in all respects except for a difference in 
phase, these systems will fail to make the proper measurements. Two signals of 
different phase will appear the same as one signal whose phase is that of the vector sum 
of the two signals. In general, the range (or the angular measurement in the interfer- 
ometer) will not correspond to either target. 

The accuracy of the interferometer antenna depends on the distance between the two 
elements. If resolution is to be obtained, the entire aperture must be filled, as with a 
closely spaced array or a reflector antenna. Similarly, in the multiple-frequency 
range-measurement technique, the accuracy is determined by the difference between 
the largest and the smallest frequency. Additional frequencies are added in between if 
the measurement is to be unambiguous. The entire spectrum must be continuous if 
targets are to be both resolved and unambiguous. By analogy with the antenna 
problem, the multiple-frequency CW radar containing N frequencies spaced A/ apart 
will produce a waveform of the form (sin JVz)/sin z, where z = rr A/T, and T is the 
transit time to the range R and back. The measurement is ambiguous when the 
denominator sin z = 0, or when A/= 1/T = c/2# unamb , which is the same as derived 
previously. 

Although the multiple-frequency distance-measuring technique was described in 
terms of a C W transmission, it can be applied to the improvement of the range measure- 
ment with a long pulse (pulse compression), as might be used for satellite tracking or 
space surveillance. 

The multiple-frequency CW radar technique has been applied to the accurate 
measurement of distance in surveying and in missile guidance. The Tellurometer is the 
name given to a portable electronic surveying instrument which is based on this prin- 
ciple. 42-44 It is capable of measuring line-of-site distances from 500 ft to 40 miles to 
within an accuracy of 1 part in 300,000 of the distance ±2 in. The Tellurometer 
consists of a master unit at one end of the line and a remote unit at the other end. The 
master unit transmits a carrier frequency of 3,000 Mc, with four single-sideband 
modulated frequencies separated from the carrier by 10.000, 9.990, 9.900, and 9.000 Mc. 
The 10-Mc difference frequency provides the basic accuracy measurement, while the 
difference frequencies of 1 Mc, 100 kc, and 10 kc permit the resolution of ambigui- 
ties. 

The remote unit at the other end of the line receives the signals from the master unit 
and amplifies and retransmits them. The phases of the returned signals at the master 
unit are compared with the phases of the outgoing signals. Since the master and the 
remote units are stationary, there is no doppler frequency shift. The function of the 
doppler frequency is provided by modulating the retransmitted signals at the remote 
unit in such a manner that a 1-kc beat frequency is obtained from the heterodyning 



CW and Frequency-modulated Radar 111 

process at the receiver of the master unit. The phase of the 1-kc signals contains the 
same information as the phase of the multiple frequencies. 

Each Tellurometer unit radiates about 100 mw of power. The antenna is a small 
paraboloid with crossed feeds to make the polarizations of the transmitted and received 
signals orthogonal to one another. This provides isolation between transmitter 
and receiver and aids in the suppression of ground reflections which can cause errors in 
the measurement. Each unit weighs less than 30 lb. 

The radar method of surveying permits long distances to be measured conveniently 
and accurately, especially over inaccessible terrain. Unlike conventional optical 
surveying instruments, it can operate by day or night and can measure distances through 
underbrush and even small trees. 

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Trans., vol. MIL-4, pp. 263-267, April-July, 1960. 
45 Varian, R. H., W. W. Hansen, and J. R. Woodyard: Object Detecting and Locating System, 

U.S. Patent 2,435,615, Feb. 10, 1948. 

46. Skolnik, M. I.: An Analysis of Bistatic Radar, Appendix, IRE Trans., vol. ANE-8, pp. 19-27, 

March, 1961. „. , ^ , , , ,« « 

47. Hastings, C. E. : Raydist: A Radio Navigation and Tracking System, Tele-Tech , vol. 6, pp. 30-33, 

100-103, June, 1947. 



4 



MTI AND PULSE-DOPPLER RADAR 



4.1. Moving-target-indication (MTI) Radar 1 

The doppler shift in frequency caused by a moving target may be used in pulse radar 
to distinguish fixed from moving targets just as in CW radar. But, it might be asked, 
why should the pulse radar be complicated by extracting the doppler information if the 
only purpose is to distinguish fixed from moving targets ? Since a pulse radar measures 
target range and angular position on each scan, moving targets may be discerned by the 
change in target position from scan to scan. Indeed, if discerning moving targets were 
the only advantage to be gained with doppler information, it would not be worth the 
trouble to instrument the radar to extract doppler. But doppler permits the pulse 
radar to discern moving targets in the presence of fixed targets even when the echo signal 
from fixed targets is orders of magnitude greater. The ordinary pulse radar which does 
not use doppler information does not have this capability. The fixed-target echoes 
with which the desired target echo must compete are those included within the same 
radar resolution cell as the target, or those which enter the radar receiver via the antenna 
sidelobes. (The radar resolution cell in this instance is the volume illuminated by a 
pulse packet.) Echo signals from fixed targets are not shifted in frequency, but the 
echo from a target moving with relative velocity v r will be shifted in frequency by an 
amount given by the doppler formula (3.2),/ d = 2v r jX, where X is the wavelength of the 
transmitted signal. The fixed targets are called clutter, an especially appropriate name 
since they tend to "clutter" the cathode-ray-tube display with unwanted information. 

The early pulse radars did not make use of the doppler information inherent in the 
echo signal from moving targets . Consequently, they were sometimes of little value in 
regions where large clutter echoes existed. But by the end of World War II the tech- 
niques and components for extracting doppler information with pulse radar were devel- 
oped. In the postwar years they were improved upon, and most modern search radars 
usually include some means of extracting the doppler information to detect moving 
targets in the presence of clutter. A pulse radar which makes use of the doppler 
information is known as an MTI radar, which stands for moving-target indication. 
It is also called pulse-doppler radar. In practice, a distinction is sometimes made 
between the MTI radar and the pulse-doppler radar, although they are both based on 
the same physical principle. MTI usually refers to a radar in which the doppler- 
frequency measurement is ambiguous but the range measurement is unambiguous. 
Another characteristic feature of the MTI radar is its delay-line canceler used to detect 
the doppler frequency shift. In the pulse-doppler radar the doppler measurement is 
usually unambiguous and the range may or may not be ambiguous. Ambiguous range 
means that multiple-time-around echoes are possible, while ambiguous doppler implies 
that "blind speeds" fall within the range of expected target speeds. The distinction 
between the two radars arose historically, and it is usually still applied. In many in- 
stances, the difference between MTI and pulse-doppler radars is only a matter of 
nomenclature. In this text the historical distinction between the two will be maintained, 
but the term MTI will be used when it is necessary to refer to the entire class of pulse 
radars which employ doppler information. 

Typically, MTI radar can extract the moving-target echo from the clutter echo even 

113 



114 Introduction to Radar Systems 



[Sec. 4.1 



if the clutter echo is 20 to 30 db greater than the moving- target echo. Some pulse- 
doppler radars can detect moving targets even when the clutter echo is 70 to 90 db 
greater than the target echo. 

A type of MT) which does not use doppler information directly is called area MTI. 
In the area MTI successive time-spaced "relief" maps of the observed area are sub- 
tracted from scan to scan. Only those objects which have changed position from one 
mapping operation to the next are displayed. Devices of this type have been success- 



r t±A 



333, 



A f <- 


cw 






V ' 


oscillator 






'Reference 


signal 


\\ > 


Receiver 




Indicator 


'J J 


f« 




(a) 








Pulse 
modulator 








" 








CW 

oscillator 

ft 


1^1 c 


Power 
amplifier 




V 






Reference signal 'j' 


;\ 






Indicator 


v ■ 






f* 



(b) 



Fig. 4.1. (a) Simple CW radar; (b) pulse radar using doppler information. 

fully developed using storage-tube techniques. 2 The area MTI using scan-to-scan 
cancellation will not be discussed further in this chapter. Instead, the major emphasis 
will be on MTI radars using sweep-to- sweep cancellation or its equivalent. 

Description of Operation. A simple CW radar such as was described in Sec. 3.2 is 
shown in Fig. 4. la. It consists of a transmitter, receiver, indicator, and the necessary 
antennas. In principle, the CW radar may be converted into a pulse radar as shown in 
Fig. 4.16 by providing a power amplifier and a modulator to turn the amplifier on and 
off for the purpose of generating pulses. The chief difference between the pulse radar 
of Fig. 4. lb and the one described in Chap. 1 is that a small portion of the CW oscillator 
power that generates the transmitted pulses is diverted to the receiver to take the place 
of the local oscillator. However, this C W signal does more than function as a replace- 
ment for the local oscillator. It acts as the coherent reference needed to detect the 
doppler frequency shift. By coherent it is meant that the phase of the transmitted signal 
is preserved in the reference signal. The reference signal is the distinguishing feature of 
coherent MTI radar. 

If the CW oscillator voltage is represented as A 1 sin 2Trf t t, where A 1 is the amplitude 
and/i the carrier frequency, the reference signal is 

V re{ = A 2 sin 2irf t t (4.1) 

and the doppler-shifted echo-signal voltage is 



^echo = A sin 



Mft±tet 



4^R 



(4.2) 



Sec - 4I J MTI and Pulse-doppler Radar 115 

where A 2 = amplitude of reference signal 

A z = amplitude of signal received from a target at a range R 
f d = doppler frequency shift 
t = time 

c = velocity of propagation 
The reference signal and the target echo signal are heterodyned in the mixer stage of the 
receiver. Only the low-frequency (difference-frequency) component from the mixer is 
of interest and is a voltage given by 

K dlff = A t sin {l^t - 4 -^^j (4.3) 

Note that Eqs. (4.1) to (4.3) represent sine-wave carriers upon which the pulse modula- 
tion is imposed. The difference frequency is equal to the doppler frequency /^. For 
stationary targets the doppler frequency shifty will be zero; hence K diff will not vary 
with time and may take on any constant value from +A t to — A iy including zero. 

L- X >( 

Hfl 



(a) 



AA A/ W 



(/>) 



^j: 



inn 



(c) 



Fig. 4.2. (a) RF echo pulse train ; (b) video pulse train for doppler frequency f d > 1/ T ; (c) video pulse 
train for doppler frequency / d < 1/ T . v 

However, when the target is in motion relative to the radar, f d has a value other than 
zero and the voltage corresponding to the difference frequency from the mixer [Eq. (4.3)] 
will be a function of time. 

An example of the output from the mixer when the doppler frequency f d is large 
compared with the reciprocal of the pulse width is shown in Fig. 4.2*. The doppler 
signal may be readily discerned from the information contained in a single pulse. If, 
on the other hand,/ d is small compared with the reciprocal of the pulse duration, the 
pulses will be modulated with an amplitude given by Eq. (4.3) (Fig. 4.2c) and many 
pulses will be needed to extract the doppler information. The case illustrated in Fig. 
4.2c is more typical of aircraft-detection radar, while the waveform of Fig. 4.2b might be 
more applicable to a radar whose primary function is the detection of extraterrestrial 
targets such as ballistic missiles or man-made satellites. Ambiguities in the measure- 
ment of doppler frequency can occur in the case of the discontinuous measurement of 
Fig. 4.2c, but not when the measurement is made on the basis of a single pulse. The 
video signals shown in Fig. 4.2 are called bipolar, since they contain both positive and 
negative amplitudes. 

Moving targets may be distinguished from stationary targets by observing the video 
output on an A-scope (amplitude vs. range). A single sweep on an A-scope might 



116 Introduction to Radar Systems 



[Sec. 4.1 



appear as in Fig. 4.3a. This sweep shows several fixed targets and two moving targets 
indicated by the two arrows. On the basis of a single sweep, moving targets cannot be 
distinguished from fixed targets. (It may be possible to distinguish extended ground 
targets from point targets by the stretching of the echo pulse. However, this is not a 
reliable means of discriminating moving from fixed targets since some fixed targets can 




Fig. 4.3. [a-e) Successive sweeps on an MTI radar A-scope display (echo amplitude as a function of 
time); (/) superposition of many sweeps; arrows indicate position of moving targets. 

look like point targets, e.g., a water tower. Also, some moving targets such as aircraft 
flying in formation can look like extended targets.) Successive A-scope sweeps 
(pulse-repetition intervals) are shown in Fig. 43b to e. Echoes from fixed targets 
remain constant throughout, but echoes from moving targets, vary in amplitude from 
sweep to sweep at a rate corresponding to the doppler frequency. The superposition of 
the successive A-scope sweeps is shown in Fig. 4. 3/ The moving targets prod uce, with 
time, a "butterfly" effect on the A-scope. 



> 



Receiver 



Delay-line 
r=V P rt 



Subtractor 
circuit 



Full-wove 
rectifier 



To indicator 



Fig. 4=4. MTI receiver with delay-line canceler. 

Although the butterfly effect is suitable for recognizing moving targets on an A-scope, 
it is not appropriate for display on the PPI. One method commonly employed to 
extract doppler information in a form suitable for display on the PPI scope is with a 
delay-line canceler (Fig. 4.4). The delay-line canceler acts as a filter to eliminate the 



Sec. 4.1] 



MTI AND PULSE-DOPPLER RADAR 117 



d-c component of fixed targets and to pass the a-c components of moving targets. The 
video portion of the receiver is divided into two channels. One is a normal video 
channel. In the other, the video signal experiences a time delay equal to one pulse- 
repetition period (equal to the reciprocal of the pulse-repetition frequency). The 
outputs from the two channels are subtracted from one another. The fixed targets with 
unchanging amplitudes from pulse to pulse are canceled on subtraction. However, the 
amplitudes of the moving-target echoes are not constant from pulse to pulse, and 
subtraction results in an uncanceled residue. The output of the subtraction circuit is 
bipolar video, just as was the input. Before bipolar video can intensity-modulate a 
PPI display, it must be converted to unipotential voltages (unipolar video) by a full- 
wave rectifier. 



»■ 



Pulse 
modulator 



TR 



fl+fc 



Klystron 
amplifier 



tf+$*£ 



Mix 



Stalo 



f? + S 



Mix 



frfd 



IF 
amplifier 



Phase 
detector 



Coho 



Reference signal 



To 
delay-line 
canceler 

Fig. 4.5. Block diagram of MTI radar with power amplifier transmitter. 

The simple MTI radar shown in Fig. 4.1Z> is not necessarily the most typical. The 
block diagram of a more common MTI radar employing a power amplifier is shown in 
Fig. 4.5. The significant difference between this MTI configuration and that of Fig. 
4.\b is the manner in which the reference signal is generated. In Fig. 4.5, the coherent 
reference is supplied by an oscillator called the coho, which stands for coherent oscillator. 
The coho is a stable oscillator whose frequency is the same as the intermediate frequency 
used in the receiver. In addition to providing the reference signal, the output of the 
coho/ c is also mixed with the local-oscillator frequency/,. The local oscillator must 
also be a stable oscillator and is called stalo, for .stable /ocal oscillator. The RF echo 
signal is heterodyned with the stalo signal to produce the IF signal just as in the con- 
ventional superheterodyne receiver. The stalo, coho, and the mixer in which they are 
combined plus any low-level amplification are called the receiver-exciter because of the 
dual role they serve in both the receiver and the transmitter. A further description of 
this type of MTI radar may be found in Ref. 3. 

The characteristic feature of coherent MTI radar is that the transmitted signal must 
be coherent (in phase) with the reference signal in the receiver. This is accomplished 
in the radar system diagramed in Fig. 4.5 by generating the transmitted signal from the 
coho reference signal. The function of the stalo is to provide the necessary frequency 
translation from the IF to the transmitted (RF) frequency. Although the phase of the 



118 Introduction to Radar Systems 



[Sec. 4.1 



stalo influences the phase of the transmitted signal, any stalo phase shift is canceled on 
reception because the stalo that generates the transmitted signal also acts as the local 
oscillator in the receiver. The reference signal from the coho and the IF echo signal 
are both fed into a mixer called the phase detector. The phase detector differs from the 
normal amplitude detector since its output is proportional to the phase difference 
between the two input signals. 

Any one of a number of transmitting-tube types might be used as the power amplifier. 
These include the triode, tetrode, klystron, traveling-wave tube, and the Amplitron. 
Each of these has its advantages and disadvantages, which are more fully discussed in 
Chap. 6. A transmitter which consists of a stable low-power oscillator followed by a 
power amplifier is sometimes called MOPA, which stands for waster-oscillator /?ower 
amplifier. 



A 










Magnetron 








3 ulse 






Trigger 
generator 


V 








oscillator 




modulator 






' 




' 




RF locking pulse 


















t 






Mix 




Stalo 




Mix 














' 


















IF 
amplifier 




Coho 












IF locking 








r 




1 

cv 


J reference 


pulse 




Phase 
detector 




signal 



To 
delay-line 
canceler 



Fig. 4.6. Block diagram of MTI radar with power oscillator transmitter. 



Before the development of the klystron amplifier, the only high-power transmitter 
available at microwave frequencies for radar application was the magnetron oscillator. 
In an oscillator the phase of the RF bears no relationship from pulse to pulse. For this 
reason the reference signal cannot be generated by a continuously running oscillator. 
However, a coherent reference signal may be readily obtained with the power oscillator 
by readjusting the phase of the coho at the beginning of each sweep according to the 
phase of the transmitted pulse. The phase of the coho is locked to the phase of the 
transmitted pulse each time a pulse is generated. 

A block diagram of an MTI radar (with a power oscillator) is shown in Fig. 4.6. A 
portion of the transmitted signal is mixed with the stalo output to produce an IF beat 
signal whose phase is directly related to the phase of the transmitter. This IF pulse is 
applied to the coho and causes the phase of the coho CW oscillations to "lock" in step 
with the phase of the IF reference pulse. The phase of the coho is then related to the 
phase of the transmitted pulse and may be used as the reference signal for echoes 
received from that particular transmitted pulse. Upon the next transmission another 
IF locking pulse is generated to relock the phase of the CW coho until the next locking 
pulse comes along. The type of MTI radar illustrated in Fig. 4.6 has had wide appli- 
cation. 1 ' 4 ' 5 

The two methods described above are not the only ones of obtaining coherent 
reference signals in the MTI. The various arrangements may be classified according to 



Sec. 4.2] 



MTI AND PULSE-DOPPLER RADAR 119 



whether (1) the transmitter locks the oscillator, or vice versa ; (2) the locking takes place 
at RF or IF; and (3) the echo and reference signals are compared at RF or IF. This 
results in eight possible combinations. 1 

4.2. Delay Lines and Cancelers 

Although the simple delay-line canceler is limited in its ability to do all that might be 
desired of an MTI filter, it has been widely used. It was one of the first practical MTI 
filter techniques developed and is usually less complex than other possible techniques. 
The delay line must introduce a delay equal to the pulse-repetition interval. Thus 
delay times as long as several milliseconds are required for typical ground-based 
surveillance radars. Delay times of this magnitude cannot be achieved with practical 
electromagnetic delay lines. The length of the electromagnetic delay path would have 
to be equal to twice the unambiguous range of the radar. This difficulty is circumvented 
by converting the electromagnetic waves into acoustic waves and accomplishing the 



PRF trigger 








Trigger 
generotor 








system 






l 












Automatic 

balancing 

circuits 














'"' ►""" AGC 












| 








. 








Carrier 
oscillator 




Delay line 




Amplifier 




Det. 






pulse 






















Canceled 






+ 






DpIo 




p[ 


















Modulator 




Subtracter 


1 


Full-wave 
rectifier 


video 








Bipolor 














Uir 


ect channe 






















Attenuation 




Amplifier 




Det. 























Fig. 4.7. Block diagram of a delay-line canceler. 

delay in an acoustical delay line. After the delay, the acoustic waves are converted 
back to electromagnetic waves. The velocity of acoustic waves depends on the delay 
medium, but it is of the order of magnitude of 10~ 5 that of electromagnetic waves; 
hence acoustic delay lines can be of manageable proportions. Both liquids and solids 
have been used as the acoustic delay media. Mercury and fused quartz are the two 
media most widely employed for MTI radar application, but water, water-glycol 
mixtures, aluminum, magnesium, and glass have also been used in delay lines. 

A block diagram of a typical delay-line-cancellation network is shown in Fig. 4.7. 
The bipolar video from the phase detector modulates a carrier before being applied to 
the delay line. The carrier frequency might be typically 1 5 or 30 Mc, but frequencies 
ranging from 5 to 60 Mc or higher have been used. The radar output is not applied 
directly to the delay line as a video signal since it would be differentiated by the crystal 
transducers that convert the electromagnetic energy into acoustic energy, and vice 
versa. The carrier frequency modulated by the bipolar video is divided between two 
channels. In one channel the signal is delayed, while in the other it proceeds undelayed. 
The signal suffers considerable attenuation in the delay line, and it must be amplified in 
order to bring it back to its original level. Since the introduction of an amplifier into 
the delay channel can alter the phase of the delayed waveform and introduce a time 
delay, an amplifier with similar delay characteristics is included in the direct (undelayed) 
channel. An attenuator might also be inserted in the direct channel to aid in equalizing 
the gain. The amplification of the direct-channel amplifier need not be as large as that 
of the delayed-channel amplifier, but the frequency response and linearity of the two 
must be similar in order to effect good cancellation. Good cancellation in a typical 
application might result in an uncanceled voltage residue of the order of 1 per cent or 



120 Introduction to Radar Systems [Sec. 4.2 

40 db. The outputs from the delayed and undelayed channels are detected to remove 
the carrier and are then subtracted. The canceled bipolar video from the subtractor is 
rectified in a full-wave rectifier to obtain unipolar video signals for presentation on the 
PPL Ideally, only moving targets produce an output from the subtractor. 

In order to maintain the gain of the two channels constant, a pilot pulse is inserted in 
the canceler. Any residue after cancellation is due to differences in channel gain or to 
the prf not being equal to the reciprocal of the delay time. The box labeled "automatic 
balancing" detects any amplitude or timing differences and generates an automatic 
gain-control (AGC) error voltage to adjust the amplifier gain and a timing-control 
error voltage to adjust the repetition frequency of the trigger generator. 

A typical transistorized MTI canceler operating at a prf of 360 pps and producing a 
cancellation ratio of 36 db may be housed in a f-ft 3 cabinet and operate on only 8 watts 
of power. 6 

Delay-line Construction. 7 ' 1 * The basic elements of an acoustic delay line are outlined 
in Fig. 4.8. The electromagnetic energy is converted into acoustic energy by a piezo- 
electric transmitting crystal. A similar transducer (the receiving crystal) at the output 



c . „ . . i crystal crystoK _ . 

End cell -»f\~\ 1 ' ' X . K~\^^ End cell 





•Transmitter Receiver 

cr 

Delay medium 

^Bonding material 
Fig. 4.8. Basic elements of an acoustic delay line. 

of the line converts the acoustic energy back to electromagnetic energy. The quartz- 
crystal transducer is normally a high-g device with an inherently small bandwidth. 
However, when the transducer is coupled to the delay medium, the medium has a 
damping effect which broadens the bandwidth. Consequently, acoustic delay lines 
are relatively broadband devices. 

The end cells enclosing the transducers may be either absorbing or reflecting. Re- 
flecting cells are more efficient and easier to construct, but they sometimes produce 
unwanted reflections which interfere with perfect cancellation. If the line is long 
enough and if the cancellation requirements are not too stringent, the unwanted 
reflections will be sufficiently attenuated by the line and may not be troublesome. For 
most applications the length of the line must be more than 1 ,000 ,asec for the secondaries 
to be attenuated sufficiently. An absorbing end cell will eliminate or reduce the 
reflections, but an absorbing end cell increases the insertion loss by 12 db (6 db per 
transducer). One absorbing cell used in the early delay lines consisted of backing the 
transducer with the same medium. Mercury end cells of this type have been used in 
operating equipments, but are not very rugged. A sturdier absorbing end cell may be 
made by soldering the transducer crystal to a solid material whose acoustic impedance 
matches that of the delay medium. For mercury, a good acoustic match can be 
obtained with a backing of hard lead. When the delay medium is solid rather than 
liquid, an additional problem is encountered in bonding the transducer to the delay 
medium. The purpose of the bonding is to provide maximum transfer of acoustic 
energy between the transducer and the delay medium. The lack of a good bonding 
material hampered the early development of the solid delay line. The discovery of a 
satisfactory bond using evaporated indium or various other cements made the solid 
delay line a practical device. 

One of the simplest acoustic delay lines consists of a straight cylindrical tube filled 
with liquid mercury. The transit time of acoustic waves in mercury at room tempera- 
ture is approximately 1 7.5 ^sec/in. To produce a delay of 1 ,000 ,«sec the line must be 



Sec. 4.2] 



MTI AND PULSE-DOPPLER RADAR 



121 




57 in. in length exclusive of end cells. This is a manageable size in a ground-based radar, 
but in those applications where space is at a premium, it is of importance to make the 
delay line as compact as possible. 

A more compact configuration may be had by folding the line back on itself one or 
more times. The acoustic signal may be reflected at the folds by two plane reflectors 
set at 45° with the path of the beam and 90° with each other. Each fold in the line 
increases the insertion loss by about 1 to 3 db. Another method of obtaining a more 
compact delay line is to make use of multiple reflections in a tank filled with liquid, as 
shown in Fig. 4.9. This technique has not proved to be too practical with liquid lines. 
The alignment of the reflecting surfaces is a problem, and it has been difficult to obtain a 
leakproof construction. Although these difficulties might be overcome, it seems that 
the net saving in weight and space with the liquid tank is not significant as compared 
with the folded line. 

Solid delay lines were not used in the early MTI radars 
because of development difficulties. These difficulties 
were surmounted, and solid delay lines are not only 
practical, but in many respects they are superior to liquid 
lines. The velocity of sound in solids is greater than that 
in mercury; consequently a slightly longer delay path is 
necessary for the same total delay time. A greater beam 
spread also results in solids because of the greater velocity. 
However, the longer delay path required in solid media 
is not a limitation since it is quite practical to construct 
a solid line to obtain multiple folded paths similar in 
cross section to that of the liquid-mercury tank of Fig. 
4.9. There is no leakage problem with the solid delay 
line, and the size and weight are less than with liquid. 
Thus the solid delay line permits comparable delay times in 
smaller packages. The most suitable solid delay medium 
has been fused quartz. Although the solid delay line 
using multiple folded paths can be constructed with a 
shape similar to the tank of Fig. 4.9, a more suitable shape is the many-sided polygon 
as illustrated by the 15-sided polygon in Fig. 4. 10. (The crystal is made with only 14 
facets since no reflections take place at one of the facets.) The signal makes 31 passes 
across the line. This is sometimes called a 15 MS-31 design. 

Solids are capable of supporting both the shear and the longitudinal mode of propa- 
gation. Since the velocity of propagation is slower in the shear mode, it is preferred 
to the longitudinal mode. This is in contrast to the liquid line, where the longitudinal 
mode is preferred. 

One of the disadvantages of either solid or liquid delay lines is the large insertion loss. 
The insertion loss of a typical folded mercury delay line with 1,000 /tsec delay is as 
follows : 8 

Impedance mismatch loss of the crystals ... 36 db 

Free-space attenuation in mercury 12.8 db 

Tubular attenuation 2.7 db 

The total insertion loss due to these three effects is 52 db. The impedance mismatch 
loss of 36 db assumes perfectly reflecting end cells. Absorbing end cells cause an 
additional 12-db loss. The attenuation in the tube is based on a smooth surface; 
rough surfaces cause additional loss. A further loss of 5 to 10 db occurs at the reflecting 
surfaces of the folded line. (There are six reflecting surfaces or three corner reflectors 
in this particular folded line.) Thus the attenuation could be as much as 70 to 75 db. 



Fig. 4.9. Volumetric delay line 
using multiple reflections in a 
tank of mercury (also similar 
to multiple reflections in solid 
delay lines). 



122 Introduction to Radar Systems 



[Sec. 4.2 



Another disadvantage of acoustic delay lines is the presence of unwanted secondary 
signals which may arise from a number of sources. One source of secondaries is the 
third-time-around signal caused by the reflections at the receiver crystal which travel 
back up the line and are again reflected by the transmitter crystal toward the receiver 
crystal. The delay path is three times that of the original delay. Further reflections 
from the receiving crystal can result in secondaries at any odd number of delay times. 
Secondaries may also be produced by such processes as conversion from one mode of 
propagation to another (longitudinal to shear mode, or vice versa), scattering by 




Input 
transducer 



Output 
transducer 



"Absorber material 
Fig. 4.10. Multiple reflections in 31-pass quartz delay line. (Courtesy Bliley Electric Company.) 

inhomogeneities within the medium, and dispersion effects. These may be eliminated 
or reduced with a straight-line delay path of large cross section. In the folded-path 
delay line using multiple internal reflections, secondaries might also appear at the 
receiving transducer because of the sidelobe radiation from the transducer's diffraction 
pattern. Radiation from the transmitter sidelobes might be internally reflected over 
some path other than the main path and find its way to the receiving transducer, where 
it may be detected by the main beam or by its sidelobes. The secondary responses are 
similar in shape to the input pulse, and they may arrive at the receiver either before or 
after the main delay. In addition to discrete secondaries, there is usually a continuous 
background of unwanted responses which bear no relationship to the shape of the input 
pulse. 

A comparison of the characteristics of a 1 ,000-^sec fused-quartz delay line and a 
mercury delay line is shown in Table 4. 1 . The operating frequency is 1 5 Mc for both 
lines. The quartz line is a 15-sided polygon as in Fig. 4.10. The signal makes 31 



Sec. 4.2] 



MT1 AND PULSE-DOPPLER RADAR 



123 



Table 4.1. Performance of l,000-/<sec Delay Lines at 15 Met 



Characteristic 


Fused quartz 


Mercury 


Insertion loss, db, into 1,000 ohms 


45 

40 

50 

6 

1 

25 

-100 

-55 to +100 


65 


Secondaries, db below main delay 


50 


Third-time-around signal, db below main delay 

3-db bandwidth, Mc 


55 
25 


Weight, lb 


8 


Size, in. 3 


34 


Temperature coefficient of delay, x 10 6 /°C 


+ 300 


Temperature range, °C 


— 38 to +80 







t Arenberg. 13 

passes. The mercury delay line is a cylinder. The insertion loss of the solid quartz 
line is less than the mercury line, the bandwidth is wider, and its size and weight are less. 
The solid line is less subject to mechanical shock and vibration as well as temperature 
variations. On the other hand, the unwanted secondary responses generated in the 
solid delay line are usually greater than in the cylindrical mercury line, and the manu- 
facturing of quartz lines may be slightly more involved than the manufacturing of 
mercury lines. The tendency in most modern MTI radars using delay-line cancelers 
is to employ the solid delay line rather than the liquid line. 

Other types of delay devices which might conceivably be used for MTI application 
are magnetic drums or disks and electrostatic storage tubes. 

Most commercial delay lines have used quartz crystals as the transducer elements. 
The quartz-crystal transducers constitute a significant portion of the total insertion loss 
(approximately 36 db out of a total of 45 db for a typical solid line using fused quartz or 
65 db for a liquid-mercury line). If barium-titanate ceramic were used for the trans- 
ducer elements rather than quartz crystals, its higher coupling coefficient would result 
in a significantly lower over-all insertion loss. An experimental delay line developed 
at the Bell Telephone Laboratories 15 using barium-titanate transducers with a fused- 
quartz delay medium resulted in a total midband insertion loss of 20 db. The length 
of this line was 1 ,000 /^sec, and it operated at a carrier frequency of 1 5 Mc with a 
bandwidth of 6.7 Mc as measured between the half-power points. The spurious 
responses were claimed to be as good as obtained with quartz-crystal transducers. 
Quartz-crystal transducers when used with solid lines are normally designed to generate 
shear waves (to reduce mode conversion), but barium-titanate transducers normally 
generate longitudinal waves, which must be converted to shear waves. This may be 
readily accomplished by reflecting the longitudinal waves off a surface at a critical 
angle which completely converts the longitudinal waves to shear waves. 

Filter Characteristics of the Delay-line Canceler. The delay-line canceler acts as a 
filter which rejects the d-c component of clutter. Because of its periodic nature, the 
filter also rejects energy in the vicinity of the pulse repetition frequency and its har- 
monics. 

The video signal [Eq. (4.3)] received from a particular target at a range i? is 

V 1 =ksin(2 1 rf d t-4^ (4.4) 

where </>„ = phase shift AnfRjc 

k = amplitude of video signal 
At a time t + T, where T = the pulse-repetition interval, the video voltage from the 
same target will be 

V 2 = k sin [iTrfit + T)- <f> ] (4.5) 



124 Introduction to Radar Systems [Sec. 4.2 

Everything else is assumed to remain essentially constant over the interval Tso that k is 
the same for both pulses. The output from the subtractor is 



v=h- 



k sin nf (l T cos 



**(. + *) 



4>o 



(4.6) 



The normalizing factor £ multiplies each video voltage since it is assumed that the power, 
and hence the video voltage, are equally divided between the delayed and the undelayed 
channels of the canceler. It is also assumed, without loss of generality, that the gain 
through the delay-line canceler is unity. The output from the canceler [Eq. (4.6)] 
consists of a cosine wave at the doppler frequency^ with an amplitude k sin irf a T. 
Thus the amplitude of the canceled video output is a function of the doppler frequency 
shift and the pulse-repetition interval, or prf. The relative frequency-response 
characteristic of the delay-line canceler [ratio of the amplitude of the output from the 
delay-line canceler, k sin (nf d T), to the amplitude of the normal radar video k] is shown 
in Fig. 4. 1 1 . The ordinate is sometimes called the visibility factor. 




Vt Vr 

Frequency 

Fig. 4.1 1 . Relative frequency response (visibility factor) of the single-delay-line canceler; T -- 
time = l// r . 



delay 



Blind Speeds. The response of the single-delay-line canceler will be zero whenever 
the argument 7rf d Tin the amplitude factor of Eq. (4.6) is 0, tt,2tt, . . . , etc., or when 



f --- 

Jd— - 



nfr 



(4.7) 



where n = 0, 1, 2, . . . 

f T = pulse repetition frequency 
The delay-line canceler not only eliminates the d-c component caused by clutter (n — 0), 
but unfortunately it also rejects any moving target whose doppler frequency happens to 
be the same as the prf or a multiple thereof. Those relative target velocities which 
result in zero MTI response are called blind speeds and are given by 



nX 
IT 



2 



= -? n = 1, 2, 3, . . . 



(4.8a) 



where v„ is the «th blind speed. If A is measured in centimeters, f r in cps, and the 
relative velocity in knots, the blind speeds are 

v =^Mi 

" 102 



(4.8&) 



The blind speeds are one of the limitations of pulse MTI radar which do not occur 
with CW radar. They are present in pulse radar because doppler is measured by 
discrete samples (pulses) at the prf rather than continuously. It will be recalled that 
the CW radar was blind to targets with zero or near-zero radial velocity. In addition, 
the pulse radar is blind to those targets whose radial velocity satisfies Eq. (4.8). If the 
first blind speed is to be greater than the maximum radial velocity expected from 
the target, the product Xf r must be large. Thus the MTI radar must operate at long 



Sec. 4.2] 



MTI AND PULSE-DOPPLER R.ADAR 



125 



wavelengths (low frequencies) or with high pulse repetition frequencies, or both. 
Unfortunately, there are usually constraints other than blind speeds which determine 
the wavelength and the pulse repetition frequency. Therefore blind speeds might not 
be easy to avoid. Low radar frequencies have the disadvantage that antenna beam- 
widths, for a given-size antenna, are wider than at the higher frequencies and would not 
be satisfactory in applications where angular accuracy or angular resolution is impor- 
tant. The pulse repetition frequency cannot always be varied over wide limits since it 
is primarily determined by the unambiguous range requirement. In Fig. 4.12, the 
first blind speed v t is plotted as a function of the maximum unambiguous range 
(/? unamb = cT/2), with radar frequency as the parameter. If the first blind speed were 
600 knots, the maximum unambiguous range would be 1 30 nautical miles at a frequency 



0,000 




. 1 \l 1 


X'W 


M 


1 \l 1 1 1 1 




1 1 1 


MIL 




- 




\ ^\. \. 








\?> 


- 










--* 




X% 


X 




1,000 






v« 


\ 


\o X > 






\ ~E 
















N. ~ 








^ \<?, NP\ 














~~ 


^%> 












\^ - 






\^> N^\° \ \ ^ 










>y _ 






\cx x&\ 


















\o \ ^ 


















\c \ 


















X ^v 














100 




i i iS 


INlk IN 


1 


\ 1 1 XI I is 




\ i iS 


INI 1 



10 100 

Maximum unambiguous range, nautical miles 



1,000 



Fig. 4.12. Plot of MTI radar first blind speed as a function of maximum unambiguous range. 

of 300 Mc (UHF), 13 nautical miles at 3,000 Mc (S band), and 4 nautical miles at 
10,000 Mc (X band). Since commercial jet aircraft can have speeds of the order of 
600 knots, and military aircraft even higher, blind speeds in the MTI radar can be a 
serious limitation. 

In practice, long-range MTI radars that operate in the region of L or S band or higher 
and are primarily designed for the detection of aircraft must usually operate with 
ambiguous doppler and blind speeds if they are to operate with unambiguous range. 
The presence of blind speeds within the doppler-frequency band reduces the detection 
capabilities of the radar. Blind speeds can sometimes be traded for ambiguous range, 
so that in systems applications which require good MTI performance, the first blind 
speed might be placed outside the range of expected doppler frequencies if ambiguous 
range can be tolerated. It is possible, in principle, to resolve range ambiguities by 
varying the pulse repetition frequency as described in Sec. 2.10. However, the neces- 
sity for resolving range ambiguities in this type of radar adds to its complexity and 
generally requires a longer time on target. Furthermore, the MTI performance will 
usually suffer. It is also possible to reduce the effects of blind speeds with a staggered 
prf as described later. 

Unambiguous doppler information (no blind speeds) as well as unambiguous range 
are simultaneously possible in a long-range ground-based search radar if the trans- 
mitted frequency is sufficiently low. For example, a radar operating at a frequency of 



126 Introduction to Radar Systems [Sec. 4.2 

100 Mc and a prf of 200 cps can achieve an unambiguous range of 400 nautical miles 
with a first blind speed of 600 knots. But at 1 00 Mc, the angular resolution is 1 00 times 
worse than it would be at 10,000 Mc (X band) for an antenna of the same size. 

Response of Single-delay-line Canceler. The maximum sensitivity of an MTI 
receiver with a delay-line canceler occurs when sin {jrf d T) = 1 [Eq. (4.6)]. When the 
doppler frequency shift is small, we may write 

Voltage response at low doppler frequencies _ . T _ tu^. .. _. 

Maximum voltage response d v x 

where v r = relative velocity of target 

v t = first blind speed 
Equation (4.9) expresses the ratio between the response of a target moving with velocity 
v r compared with maximum response. As an example, consider (as does Ridenour 1 ) a 
radar operating at a wavelength of X = 9.2 cm with a pulse repetition frequency 
f r = 2,000 cps. The first blind speed computed from Eq. (4.8) is 180 knots. A 
thunderstorm moving at a relative velocity of 30 mph (26 knots) will produce a response 
7 db below the maximum. In other words, if the echo from the cloud were 7 db 
greater than the echo from the target, both would appear to be of equal strength at the 
output of the delay-line canceler. Thus we may conclude that this type of performance 
is not good enough to eliminate the slowly moving cloud. Experience has confirmed 
that MTI radars with the type of characteristics as illustrated by the above example do 
not eliminate as much of the storm clutter as might be desired. The delay-line filter 
characteristic should have more attenuation in the vicinity of zero doppler frequency, 
as in the double-delay-line canceler discussed later. 

If the target is assumed to be of constant cross section and can have any radial 
velocity with equal probability, it is of interest to ask what is the probability of the 
target being detected with the MTI radar as compared with the probability that it will 
be detected with a normal non-MTI radar. It is assumed for purposes of comparison 
that the maximum sensitivity of the MTI radar (i.e., when nf d T = mi) is the same as the 
non-MTI radar sensitivity. It is also assumed that the signal strength (power) received 
by the MTI radar at maximum response is K times the minimum detectable signal. 
(The problem of defining the minimum detectable signal is ignored here since it is the 
relative performance between MTI and non-MTI radars which is of interest.) The 
relative (voltage) response of the MTI radar when the target radial velocity is other 
than that corresponding to maximum response is 

Relative (voltage) response = Vk sin {jrf d T) (4.10) 

The target will be detected by the MTI radar whenever Eq. (4.10) is equal to or greater 
than unity. The probability that the signal will be detected by the MTI radar com- 
pared with the probability that it will be detected by the non-MTI radar is 

Relative probability = */2 - sin^O/V*) (4 ., 1} 

77-/2 

This is plotted in Fig. 4.13. It represents the fraction of time Eq. (4.10) is greater than 
unity, assuming all values of doppler are equally likely. It should be cautioned that 
this simple analysis of the relative detection capability is only an approximation. No 
definition has been given for minimum detectable signal, nor is the assumption that all 
doppler velocities are equally likely a good one in all circumstances. Although Fig. 
4.13 shows that the performance of the MTI radar is not as good as a radar without 
MTI, it should be remembered that this applies to a target in the absence of clutter 
("in the clear"). An MTI radar will maintain its performance in those situations 



Sec. 4.2] MTI and Pulse-doppler Radar 127 

where the effectiveness of the normal non-MTI radar is drastically reduced by the 
presence of large clutter echoes. 

Probability of Obtaining a Particular Radial Velocity. The assumption used above 
that all radial velocities are equally likely may not always be realistic, although it is a 
convenient one and probably as good an assumption as any if there is no prior knowledge 
of target behavior. In this section the radial- velocity probability-density function for 
two different target assumptions will be derived. 




10 20 30 40 50 

K= ratio of MTI echo signal power to non-MTI 

minimum detectable signal 



Fig. 4.13. Plot of Eq. (4.11). Relative detection probability of a single-delay-line canceler MTI as 
compared with a non-MTI radar (all doppler frequencies assumed equally likely, with the target "in 
the clear"). 



Target 



case 1 : target with constant velocity. It is assumed that the target velocity v is 
constant and that the target trajectory makes an angle 6 with the axis of the radar beam 
as shown in Fig. 4.14. All values of the angle d are assumed 
to be equally probable. (Any angle is just as likely to be 
observed as any other angle.) The relative velocity is v r = 
v cos 0. It is desired to find the probability-density function 
for the relative velocity, that is, the probability that the rela- 
tive velocity will lie between the values of v r and v r + dv r . 

This is a problem in determining the change in the prob- 
ability-density function with a change in variable. The tech- 
nique involved is standard in probability theory. A concise 
explanation is given, for example, by Bendat. 16 If there is a 
functional relationship between two random variables y =f{x), 
assumed single-valued, and a one-to-one correspondence 
between y and x, then the probability-density function for p(y) is related to the 
probability-density function for p(x) by 




Radar 



Fig. 4.14. Geometry of 
radar and target. 



p(y) dy = p(x) dx 

or p(y) = — — 

dy/dx 

If each value of y corresponds to n values of x, then 

np(x) 



P(y) = 



dy/dx 



(4.12a) 
(4.12b) 

(4.13) 



128 Introduction to Radar Systems [Sec. 4.2 

In our example the probability-density function for the angle 6 is given by 

1*0) = r (4.14) 

ATI 

since 6 is equally likely over the range from to 2n. We wish to findp(v r ). Each value 
of v r corresponds to two distinct values of (+0 and — 0), so that 



P(v r ) = 



2p(6) 
dv r jdB 



1 



1 



1 



ttv sin 6 



v r <v (4.15) 



The minus sign obtained on differentiation is ignored since probability-density functions 
must always be positive. A plot of this equation is shown in Fig. 4. 1 5. 

CASE 2 : TARGET VELOCITY BETWEEN D min AND 

ttmax- When the target velocity v and the angle 
are both random independent variables, the 
joint probability-density function for v and v r 
is 

p(v,v r ) = p(v)p(v r ) (4. 1 6) 

The angle is again assumed to be equally 
likely over the interval to 2w, while the target 
velocity is assumed to lie anywhere within the 
range v min to v max . Therefore p{v) = (t> max — 
tfmin) -1 and p(v r ) is given by Eq. (4.15). To 
find the probability-density function for v r , Eq. 
(4. 1 6) must be integrated over the variable v. 




PlO>r) 



p(v,v r )dv (4.17) 



0.4 0.6 

Fig. 4.15. Probability-density function of 
v„ assuming constant velocity and all 
angles equally likely. 

Because v r can never be greater than v, the 
integration is divided into two parts. When v r < i>min, the variable v r within the 
integral will never exceed v, and 






PiiPr) = 



1 






(l> 2 - I*?)-* dv 



■"■(^max ^min) ""min 

= -(cosh-i ^22 - cosh" 1 ^) 

When v r lies within the limits of integration v min and v m& 

1 /""max . 1 

fc<«v) = - — - — - (v 2 -viy i dv= l 

7r(l>max — fminj J» r 



for < V r < V n 



(4.18) 



cosh 



-1 "max 



7r(l) m ax — ^min) V r 

for y min <V r < Umax 



(4.19) 



A plot of the probability-density function as given by Eqs. (4.18) and (4.19) is shown in 
Fig. 4.16. If the relative velocities are distributed according to Eq. (4.19), instead of 
uniformly as assumed in the derivation of Eq. (4.11) or of Fig. (4.13), the over-all 
target-radar response characteristic for the simple-delay-line canceler may be obtained 
by multiplying the ordinate of Fig. 4.1 1 (with relative velocity instead of frequency as 
abscissa) and a curve similar to Fig. 4.16, but with the appropriate values of v mln and 



Sec. 4.2] 



MTI AND PULSE-DOPPLER RADAR 



129 



Multiple and Staggered Pulse Repetition Frequencies. The blind speeds of two 
independent radars operating at the same frequency will be different if their pulse 
repetition frequencies are different. Therefore, if one radar were "blind" to moving 
targets, it would be unlikely that the other radar would be "blind" also. Instead of 
using two separate radars, the same result can be obtained with one radar which 
time-shares its pulse repetition frequency between two or more different values {multiple 
prf 's). The pulse repetition frequency might be switched every other scan or every time 
the antenna is scanned a half beamwidth, or the period might be alternated on every 
other pulse. When the switching is pulse to pulse, it is known as a staggered prf. 17 




Fig. 4.16. Probability-density function of relative velocity, assuming target velocities distributed 
uniformly from v min to v mBK . 

An example of the composite (average) response of an MTI radar operating with two 
separate pulse repetition frequencies on a time-shared basis is shown in Fig. 4. 1 7. The 
pulse repetition frequencies are in the ratio of 5 :4. Note that the first blind speed of 
the composite response is increased several times over what it would be for a radar 
operating on only a single pulse repetition frequency. Zero response occurs only when 
the blind speeds of each prf coincide. In the example of Fig. 4. 1 7, the blind speeds are 
coincident for 4/7\ = 5/r 2 . Although the first blind speed may be extended by using 
more than one prf, regions of low sensitivity might appear within the composite 
passband. 

One method of obtaining the second pulse repetition frequency is to add to the MTI 
delay line in the cancellation network a short section of line that is switched in and out 
of the system periodically. In addition to changing the length of the delay line, the 
pulse-repetition interval of the transmitted signal must also be changed. 

Switching may be accomplished every scan, every half beamwidth, every pulse, or 
some other convenient grouping of pulses. Although switching of the repetition 
period on every alternate pulse may be convenient, it is not always advisable if the 
possibility of large second-time-around clutter echoes exists. A second-time-around 
clutter echo will not cancel in the delay line when the prf's are staggered pulse to pulse. 



130 



Introduction to Radar Systems 



[Sec. 4.2 

Echoes might result that could be taken for those of a moving target. Observation of 
second-time-around echoes over several scans will show whether the target is in motion 
or is stationary and may be ignored. Nevertheless, one should carefully consider the 
effect of second-time-around echoes before specifying staggered prf 's. The reason 
second-time-around echoes do not cancel is described below. 




Frequency 
(i) 




Fig. 4.17. (a) Frequency-response characteristic (visibility factor) for/, 
l/T^; (c) composite frequency response with 7i/r 2 = i. 



1/Ti; (6) same for/. 



Trigger to 
modulato 



Bipolar 
video 






Ganged switches-M 



Delay line 

€ 



PRF generator 
period T 



Delay-line canceler 
delay T 



_Canceled 
"video 



Fig. 4.18. Means for generating a staggered prf. 

Consider the simple block diagram in Fig. 4.18, which illustrates that portion of the 
radar which might be used to produce a pulse transmission staggered every other pulse. 
The prf generator output is a steady train of pulses with a uniform interval T. These 
pulses trigger the modulator, which, in turn, fires the transmitter. The trigger pulses 
are alternately switched between an undelayed path and a short section of delay line of 
length e. The period between the transmitted pulses is alternately T — e and T + e as 



Sec. 4.2] 



MTI AND PULSE-DOPPLER R.ADAR 



131 



shown in the timing relationships of Fig. 4.19a. The target echo returns after a time 
T r , as shown. In those periods where the transmitted pulse was delayed, the received 
echo would be undelayed. Conversely, in those periods where the transmitter trigger 
pulse was undelayed, the received echo would be delayed by an amount e. Therefore 
target echoes at the input to the delay line {B in Fig. 4. 1 8) appear from pulse to pulse at 
the same time with respect to the trigger pulses. The delay line in the canceler is of 
length T. The received pulses are delayed an amount e in addition to their transit time 
T r . This additional delay e may be readily accounted for in the timing circuits. 



Basic PR 



Transmitter 
trigger 



, 1 1 



T+t — H*— T-t- 



-*)£ 



LJ 



-r+e 



— h 



L 



i i I i 



Received echo 
at/3 



T 



Received echo J 7^ ^ ->U+cfr- -j T r +t \- -\T r +c\ - 



<«) 



h— r > \ ' r- 



Basic PRF 



Transmitter 
trigger 



H r+e- 



-J 



Received echo I 
at/J I 



Received echo I 
ot B I 



-J 



t-r-*-i| 

Jb L 



^ih- h^-i -jfrh- 



i I 



-j. 



-&*-i 



t 



(A) 

Fig. 4.19. Timing relationships in staggered prf MTI radar, (a) Normal, fixed-clutter target; (/>) 
second-time-around clutter target. 



When a second-time-around target appears, the pulse-to-pulse echoes do not have 
the same time relationship at the input to the delay-line canceler. Therefore an 
uncanceled residue results, just as if the target were in motion. This is illustrated by 
the timing relationships in Fig. 4.196. 

In addition to the extra equipment required of the staggered-repetition-rate MTI 
radar, the data rate (number of hits per scan) is effectively lowered because of the time 
sharing between the two frequencies. 

Another method of generating a staggered prf using a recirculating trigger pulse (as 
described later in Fig. 4.32) is shown in Fig. 4.20. 



132 Introduction to Radar Systems [Sec. 4.2 

Double Cancellation. The frequency-response function of a single-delay-line 
canceler (Fig. 4. 1 1) does not have as broad a clutter-rejection null as might be desired in 
the vicinity of d-c or at doppler frequencies corresponding to the prf and its harmonics. 
The clutter-rejection notches may be widened by passing the output of the delay-line 



PRF- 



Bipolcr 
video 



Modulator 



Trigger 
generator 



Pulse 
amplifier 



[Switching 



Delay I 



line _J 



Delay line 
T 



Det. 



Undelayed channel 



Det. 



in 



Subtractor 



Canceled 
video 



Fig. 4.20. Means for generating a staggered prf with a recirculating pulse. 

canceler through a second delay-line canceler (Fig. 4.21a). In the double-delay-line 
canceler, the output from the single-delay-line canceler 



V= fcsimr/^Tcos 



2-nL 



(■+{)-*; 



is subtracted from the canceler output V from the pulse period Tsec earlier. 



V = k sin tt/jTcos 



:eler is the difference \ 
= k sin 2 nf d T sin [2irf^t + T) - <£ ] 



(4.6) 



(4.20) 



The resultant output from the second canceler is the difference between Kand V . 

V-V _ „ 

(4.21) 

The amplitude of the double canceler compared with a non-MTI radar has a sine- 
squared shape (Fig. 4.22) rather than the sine-wave response of a single-delay-line 



Input 



■€ 



Deloy line /"=V/ r 




Delay line T-\/f r 



Output 



Input 



_r 



Delay line T-% 



Delay line T=Vf r 



-2 




Output 



Fig. 4.21. (a) Double-delay-line canceler; (b) three-pulse-comparison canceler. 

canceler. Double cancellation requires more equipment and results in a slight reduc- 
tion in response for moving targets. Note that the double-delay-line frequency- 
response characteristic is the square of the single-delay-line characteristic. This may 
be seen by inspection since the double-delay-line canceler is simply two single-delay-line 
cancelers in cascade. 

The two-delay-line configuration of Fig. 4.21* has the same frequency-response 
characteristic as the double-delay-line canceler. The operation of the device is as 
follows. A signal f(t) is inserted into the adder along with the signal from the 



MTI AND PULSE-DOPPLER RADAR 



133 



Sec. 4.2] 

preceding pulse period, with its amplitude weighted by the factor —2, plus the signal 
from two pulse periods previous. The output of the adder is therefore 

f{t) - 2f(t + T) +f(t + IT) 

which is the same as the output from the double-delay-line canceler 

f{t) -/(/+ T) -fit + T) +fit + IT) 

This configuration is commonly called the three-pulse-comparison canceler. The 
three-pulse-comparison canceler is equivalent to the delay-line canceler only so long as 
they are both in perfect adjustment. If the circuits drift out of adjustment because of 
aging of components or some other cause, the double-cancellation network will not 
deteriorate as rapidly as the three-pulse-comparison network. If either one of the two 




Fig. 4.22. Frequency response of single-delay-line canceler (solid curve) and double-delay-line canceler 
(dashed curve). Shaded area represents clutter spectrum. 

cancellation networks which constitute the double canceler drifts out of adjustment, the 
other is still capable of canceling stationary clutter, and if both are out of adjustment by 
a small amount, the residue which is left is the product of two small quantities and is 
also a small quantity. On the other hand, in the three-pulse-comparison network, any 
drift in the pulse amplitudes from their correct values results in a first-order lack of 
cancellation. Another advantage of the double canceler over the three-pulse-com- 
parison canceler is that each section can be adjusted separately. 




Fig. 4.23. Canonical-configuration comb filter. (After White and Ruvin, w IRE Natl. Cortv. Record.) 

Shaping the Frequency-response Characteristic. The ideal MTI filter characteristic 
is one which rejects the clutter spectrum without eliminating any moving targets. The 
ideal characteristic is not achievable in practice, but it is possible to obtain delay-line 
filters with frequency characteristics more suitable than the sine or the sine-squared 
characteristic of Fig. 4.22. The techniques for synthesizing delay-line filters with 
almost any desired frequency response have been described in the literature. 18-20 The 
basic technique employs a number of delay lines in cascade with feedback and feed- 
forward paths (Fig. 4.23). This general configuration may be used to implement any 
realizable filter, and because of this property, it is called the canonical configuration. 18 



134 Introduction to Radar Systems 



[Sec. 4.2 




1 2 3 

Angular frequency, oj 

(a) 



1.0 

0.5 






(i>) 



1A 



-S 0. 




"0 1/7" 

Frequency 

W) 
Fig. 4.24. (a) Three-pole Chebyshev low- 
pass filter characteristic with 0.5-db ripple 
in the passband ; (6-rf)delay-line filter charac- 
teristics derived from (a). (After White, 1 " 
Proc. Natl. Con/, on Aeronaut. Electronics.) 



The canonical configuration is useful for 
conceptual purposes, but it may not always 
be desirable to design a filter in this manner. 
White and Ruvin 18 state that the canonical 
configuration may be broken into cascaded 
sections, no section having more than two 
delay elements. Thus no feedback or feed- 
forward path need span more than two delay 
elements. This type of configuration is some- 
times preferred to the canonical configuration, 
as, for example, the case of the double can- 
celer vs. the three-pulse-comparison canceler. 
Ideally the two are equivalent. But if the 
delay lines are not in perfect adjustment, the 
three-pulse-comparison canceler (an example 
of the canonical configuration) gives poorer 
performance than the double canceler (an 
example of cascaded sections). 

The synthesis technique described by White 
and Ruvin may be applied with any known 
low-pass filter characteristic, whether it is a 
Butterworth, Chebyshev, or Bessel filter or 
one of the filters based on the elliptic-function 
transformation which has equal ripple in -the 
rejection band as well as in the passband. An 
example of the use of these filter character- 
istics applied to the design of a delay-line 
periodic filter is given in either of White's 
papers. 18 - 19 Consider the frequency-response 
characteristic of a three-pole Chebyshev low- 



pass filter having 0.5 db ripple in the pass- 
band (Fig. 4.24). The three different delay-line-filter frequency-response character- 
istics shown in Fig. 4.24/3 to d were derived from the low-pass filter characteristic of 
Fig. 4.24a. This type of filter characteristic may be obtained with a single delay line 
in cascade with a double delay line as shown in Fig. 4.25. The weighting factors 
shown on the feedback paths apply to the characteristic of Fig. 4.24c. 




Fig. 4.25. Form of the delay-line filter required to achieve the characteristic of Fig. 4.24c. 



Another example of a delay-line periodic filter with adjustable frequency response 
is the double-loop, single-delay-line canceler (Fig. 4.26). Its frequency-response 
characteristic is 20 



H(f) = 



exp (jlvjT) - 1 



exptpTr/D-fc 
Equation (4.22) is plotted in Fig. 4.27 for various values of the feedback factor k. 



(4.22) 



SeC - 4 - 2 ] MTI AND PULSE-DOPPLER RADAR 135 

Cancellation at IF. 1 It is possible, in principle, to perform the delay and cancellation 
in the IF rather than the video portion of the radar receiver (Fig. 4.28). The two IF 
signals of amplitude V IF subtracted by the canceler are 



v i = ^if sin 



V, = Kp sin 



M/JFi/i)*- 



Wht*o" 



MflF ±f d )(t+T)- 



WifRo' 



One-half the difference between these two signals is 



V d = V lF sin [tt(/ if ±f d )T~] cos 
The output of the phase detector is a voltage 



2H/if± /„)(' + j) -^^2 



(4.23) 
(4.24) 

(4.25) 



V v =± kV lF sin [t7(/ if ±/ d )T] cos \2tt 



±f i t + UiY±f i )- 



_j^R^ (426) 



The video voltage is at the doppler frequency /,, and has an amplitude proportional to 

sin7r(/ IP ±/,)r (4.27) 



Canceled output 




Fig. 4.26. Double-loop, single-delay-line canceler; 1 — k = amplifier gain. 
Trans.) 



(After Urkomtz, 20 IRE 



Unlike normal video cancellation, cancellation at IF involves a residue which is a 
function of the intermediate frequency times the time delay (f w T). When there is no 
doppler frequency shift, f d = 0, but the ampli- 
tude of the canceled signal [Eq. (4.27)] will not 
be zero unless Trf lv T = 0, tt, 2tt, . . . , or/ IF = 
n/T = nf r , n = 0, 1, 2, 3, . . . . Hence a require- 
ment of the IF delay-line canceler is that the 
intermediate frequency must be an integral mul- 
tiple of the prf. In addition, it is also necessary 
that the delay line be more accurate than with 
video cancellation. With the video canceler, it 
is only necessary that the time delay be accurate 
to within a fraction of the pulse width (of the 
order of 1 per cent for 40-db cancellation), while 
in the IF canceler the delay time must be accurate 
to within a fraction of the period of the intermed- 
iate frequency. If the delay time were to vary by 
one-half of an IF period, the two signals reinforce rather than cancel. These 
two additional requirements imposed upon the IF canceler are not present with the 
video canceler and have, in the past, limited the application of IF-canceler circuits. 




Frequency 



Fig. 4.27. Response shaping of double- 
loop, single-delay-line canceler of Fig. 
4.26 with changing feedback factor k. 
(After Urkowitz, 20 IRE Trans.) 



136 Introduction to Radar Systems 



[Sec. 4.2 



Similar considerations apply to performing the subtraction at the carrier frequency 
in the video delay-line canceler, that is, by subtracting the delayed and the direct signals 
before the carrier is removed. 



Received 
signal 
from 
mixer 











Reference signal 


J 






Delay line 


~L 




, f 






IF 
amplifier 








Subtracfor 


, Phase 






r* 


detector 












- 











Canceled 
" video 



Fig. 4.28. Block diagram of IF delay-line canceler. 



FM Delay-line Cancellation? 1 The delay-line canceler of which Fig. 4.7 is an example 
is sometimes called an AM (amplitude-modulation) delay-line canceler. The relative 
gain stability between the delayed and the undelayed channels must be maintained 
within close limits if perfect cancellation is to result. Thus the two channels of AM 
delay-line cancelers must be maintained in perfect gain adjustment, which is one of its 
chief limitations. This disadvantage may be alleviated by converting the video 
amplitude variations into frequency variations. The frequencies of the delayed and 
the undelayed signals are compared, and any differences in frequency correspond to 
differences in amplitude. This is called FM (frequency-modulation) cancellation. 
The advantage of the FM canceler is that it is easier to keep in adjustment since gain 
variations between the two channels are not as important as with the AM canceler. 



Bipolor 
video 

from — 
phase 
detector 



1 

FM 








Direct 


oscillator 








channel 




' 










Delay 
line 





Phase 
detector 



Delay 
amplifier 



Differentiation 
circuit 



Canceled 
-*■ bipolar 
video 



Fig. 4.29. FM delay-line canceler using phase detector. 

There are two types of FM cancellation systems. One is called phase-detector 
cancellation, and the other is called two-mixer cancellation. The block diagram of the 
phase-detector cancellation circuit is shown in Fig. 4.29. An oscillator (such as a 
reactance-tube oscillator) is frequency-modulated according to the amplitude of the 
bipolar video. The frequency-modulated signal is divided between the delayed and the 
direct channels, and the two outputs are compared in the phase detector. The output 
of the phase detector is passed through a differentiating circuit. The differentiated 
output is proportional to the difference in frequency between the two signals and thus is 
a measure of the uncanceled amplitudes of two successive video pulses. The output of 
the differentiating circuit is of the same form as the output of the AM delay-line canceler 
[Eq. (4.6)]. A full-wave rectifier inverts the negative pulses before the canceled video 
is applied to the PPI. 

The block diagram of the two-mixer FM cancellation system is shown in Fig. 4.30. 
The video signal modulates the reactance-tube oscillator centered at frequency f . 
One portion of the frequency-modulated signal is delayed, amplified, and fed into 
mixer 2. In the undelayed channel the modulated signal centered about f Q is mixed 
with the output of a stable CW oscillator of frequency^ in mixer 1 to obtain a modulated 
signal centered about a carrier f + f v The outputs from the two channels are 
heterodyned in mixer 2 to obtain a frequency-modulated signal centered about /j. 
This frequency-modulated signal is limited and applied to a discriminator to convert its 
frequency variations to amplitude variations. The output of the discriminator is 
proportional to the amplitude differences between two successive pulses. 



Sec. 4.2] MTI and Pulse-doppler Radar 137 

The phase-detector canceler is the simpler of the two, but it requires high driving 
voltages for the phase detector if the system is to be broadband. Also, if double 
cancellation is desired, phase-detector cancellation presents additional complexities. 
The two-mixer cancellation can be used directly in double-cancellation MTI, thus 
eliminating a second reactance-tube deviable oscillator. 



Bipolar 
video 
from — 9 
phase 
deteetor 



FM 
oscillator 



Stable 

CW 

oscillator 




f\ 




■ 


/i 








Mixer 
No.t 


%+f\ 


Mixer 
No. 2 


Limiterond 
discriminator 














, 


fo 




Delay 
line 




Delay 
amplifier 













Conceled 
- bipolor 
video 



Fig. 4.30. FM delay-line canceler using two mixers. 

An example of an FM double-cancellation network 2 using a single delay line is 
shown in Fig. 4.31 . In the diagram two delay lines are shown, but only a single line is 
used in practice. On one pass the delay line operates at the fundamental of the crystal 
transducer (30 Mc), while on the second pass the crystals are driven at the third har- 
monic (90 Mc). This canceler is slightly different from that shown in Fig. 4.30 in that 
mixer 1 is in the delayed channel in Fig. 4.31 and in the undelayed channel of Fig. 4.30. 





30-Mc 
oscillator 












1 




90-Mc 
delay line 




Posfdelay 
amplifier 


90 Mc 


Mixer 
No. 1 


Bipolar 










video 


FM 
oscillator 


90 Mc 














m > 















60 Mc 



Mixer 
Mo. 2 



30 Mc 

















90 Mc 












30 Mc 














1 














Mixer 
No. 2 


45 Mc 


Limiter and 
discriminator 






30-Mc 
delay line 




Postdelay 
amplifier 




Mixer 
No. 1 














30 Mc 


75 Mc 












\ 






45-Mc 
oscillator 





Double 

canceled 

video 

out 



Fig. 4.31. FM single delay line used for double cancellation by operating at the fundamental and the 
third harmonic of the crystal transducer. {After Solomon? 1958 Proc. IRE Conf. on Military Elec- 
tronics.) 

The ability of the FM canceler to attenuate fixed clutter signals is probably no better 
than the AM canceler. Both types are capable of reducing clutter by about 30 to 35 db. 
However, the advantage of the FM canceler is that it does not require the continual 
adjustment necessary with the A M canceler in order to maintain maximum performance. 

Generation of the Pulse Repetition Frequency. 1 If the delay time and the pulse 
repetition period are not exactly equal, perfect cancellation cannot be expected from the 
delay-line canceler. In general, it is not difficult to maintain a stable prf, but it is not 



138 



Introduction to Radar Systems 



[Sec. 4.2 

always easy to achieve a stable delay line. One reason the delay time might change is 
that the velocity of propagation of the delay medium is a function of the temperature. 
The velocity of sound waves in mercury will change by 1 part in 3,300 for a change 
in temperature of 1 °C. The velocity change in fused quartz is 1 part in 1 0,000 for a 1 °C 
change.j If a maximum temperature variation of 50° were anticipated, the total delay 
time would vary by 1.5 per cent in mercury and 0.5 per cent in fused quartz. The total 
time delay may also be influenced by the rest of the circuitry involved in the delay-line 
canceler. Time delays introduced by the circuitry (other than the delay line) in the 
delayed channel of the canceler must be balanced with equal time delay in the undelayed 
channel. 



Bipolar 
video 



Modulator 





D 


4 




D 


3 








Trigger 
generator 


— < — 


Pulse 
amplifier 






' 








Di 








, 


0, 








Delay line 






Postdelay 
amplifier 




Def. 








*1 




f 










Subtracter 


Direct channel 0% 


Det. 


J 





























Canceled 

bipolar 

video 



Fig. 4.32. Use of the delay line to establish the prf. 

The pulse-repetition period and the delay time may be maintained equal to one 
another by either adjusting the length of the delay line to the pulse-repetition interval or 
by using the delay line to generate the prf. In the former method a stable oscillator 
generates the prf and the delay line is made of variable length so that it may be adjusted 
to match the pulse-repetition period. A variable-length delay line may be constructed 
using a straight cylindrical tube filled with liquid and having a telescoping section. 
This technique was used in several early MTI systems. 

The delay line itself may establish the pulse repetition frequency by circulating a 
trigger pulse around the delay line as illustrated by the block diagram of Fig. 4. 32. The 
rate at which the trigger pulse circulates about the delay line determines the prf. Two 
separate delay lines adjacent to one another enclosed, within the same environment, may 
be used to generate separately the prf and to provide the delay for MTI cancellations. 
Or alternatively, a single line may be used for both functions. 

The pulse-repetition period Tis determined by the total delay time around the loop 
which contains the delay line D lt pulse amplifier Z> 3 , and trigger generator Z> 4 , or 



T = D t + D 3 + D t 



(4.28) 



For perfect cancellation, the difference in the time delays in the delayed and undelayed 
channel must also equal T, or 

T= D l + D 1 - D 2 (4.29) 

The delays in the trigger pulse amplifier D 3 can be made small, and D 3 plus the delay D 2 
will usually be of the order of Z> 1; so 



D 3 + D z ^ D 1 



(4.30) 



The result is that the trigger-generator delay D 4 must be zero, a condition which cannot 
be met in practice. The delay time of a typical trigger generator such as a blocking 

t Special glass delay lines can be obtained with temperature coefficients of time delay less than 
1 ppm/°C. 3 ' 



Sec. 4.2] 



MTI AND PULSE-DOPPLER RADAR 



139 



oscillator might be of the order of 0. 1 ^sec. One technique for compensating for the 
time delay in the trigger generator is to increase the time delay D 1 with a length of 
electrical delay line as shown in Fig. 4.33. The use of an electrical delay line is a simple 
"Solution to the problem. The electrical delay line may operate at either the carrier 
frequency or the video frequency, but it is usually inserted in the video because video 
delay lines are easier to achieve than carrier-frequency lines. 



PRF-*- -. 




Trigger 
generator 


— < — 


Pulse 
amplifier 








' 










. 














Acoustic 
delay line 


>■ 


Postdelay 

amplifier 






Defector 


— *— 


Electrical 
delay line 




Bipolar 








1 




video 


Modulator 




















Subtracfor 








Direct chonnel 


Detector 


1 

























Canceled 

bipolar 

video 



Fig. 4.33. Use of short piece of electrical delay line to compensate for the time delay of the trieeer 
generator. ' 5& 

The additional delay in D 1 may also be obtained acoustically by adding to the delay 
line a second receiving crystal at the appropriate distance from the output end of the 
line (Fig. 4.34). A 45° reflector, analogous to the half-silvered mirror of optics, is 
placed in the mercury delay line just before the normal output crystal to reflect a portion 
of the acoustic energy into a second output crystal. The position of the reflector may 
be made adjustable so as to vary the compensating delay. 

When the same delay line is used for both MTI cancellation and for generating the 
prf, some means must be had for distinguishing the trigger pulse from the echo signal. 
The discrimination may be made on the basis of time selection or amplitude selection. 



PRF- 



Bipolar 
video 



Modulator ■»- 



Trigger 
generator 



Pulse 
amplifier 



Acoustic delay line 



lelay line Is 



Postdeloy 
3 ' I amplifier 



Def. 



■ Half-silvered" 
mirror 



n. 



Det. 



Subtractor 



Conceled 

bipolar 

video 



Fig. 4.34. Use of half-silvered mirror in mercury acoustic line to compensate for the additional time 
delay in the trigger generator. 



Another technique is to use a different carrier frequency for the trigger pulse than that 
used for the echo signal. This is made possible by the large bandwidth of delay lines. 
The trigger generator must be self-starting, and it must be designed so that, once fired, 
it will not trigger additional pulses until the next pulse interval. Usually the recovery 
time constant of the trigger generator is made at least one-half the pulse-repetition 
period (Tj2). A blanking gate of duration T/2 may also be applied to the pulse amplifier 
for additional reliability. 

The pulse repetition frequency can be generated with a second acoustic delay line 
similar to that used for cancellation except that the prf delay line should be slightly 
shorter (on the order of a microsecond) to compensate for the delay Z> 4 in the trigger 
generator. The two delay lines should be operated side by side so that any changes 
which take place in the thermal environment will affect both lines equally. This 



140 



Introduction to Radar Systems 



[Sec. 4.3 



arrangement is straightforward, but it requires increased space and weight because of 
the necessity of two lines. 

Still another technique for equalizing the MTI delay time and the pulse-repetition 
period makes use of both the stable prf oscillator and a circulating signal in the delay 
line (Fig. 4.35). This method has been called electronic frequency tracking. The 
stable oscillator must be tunable. The coincidence circuit compares the time of occur- 
rence of the nth pulse from the delay line with the (n + l)st pulse fed into the line. If 
the nth pulse (delayed) and the (n + l)st pulse (undelayed) are coincident, the prf and 
the MTI delay line are in synchronism. If the two pulses are not coincident in time, the 
time difference is converted to a voltage which is used as an error signal to change the 





PRF 

t 






Turable, 

stable 

PRF 

oscillator 










I 












Coincidence 
circuit 


















, 












. 


. 


video 

— > — 


Modulator 


-»- 


— 


Delay line 




Postdeloy 
amplifier 


— ' 


— 


Det. 


1 




Canceled 
bipolar 






^ 


' 










Subtractor 


video 

— *- 




Direct channel 


Det. 


J 



























Fig. 4.35. Generation of the prf with frequency tracking. 



frequency of the prf oscillator in a direction which will bring the two pulses in coinci- 
dence. The advantages of this technique are that any drift in the delays of the cancel- 
lation loop are automatically compensated and there are no additional mechanical 
parts. Its disadvantages are that the prf oscillator must remain stable with no jitter, and 
a relatively large number of tubes or transistors is required as compared with other 
techniques. 

4.3. Subclutter Visibility 

In the discussion of the delay-line canceler it was assumed that the echo signal from 
stationary clutter was fixed and did not vary in either amplitude or phase from pulse to 
pulse. In practice, however, clutter echoes are not always stationary; they may be in 
motion so as to produce an uncanceled residue at the output of the delay-line canceler. 
This uncanceled residue might be mistaken for a moving-target signal. In addition to 
the internal motion of clutter, a residue at the output of the delay-line canceler may 
result from instabilities in the transmitting or receiving equipment or from changes in 
amplitude from pulse to pulse due to the shape of the antenna pattern. 

A measure of the performance of an MTI radar is the subclutter visibility, which is 
defined as the gain in signal-to-clutter power ratio produced by the MTI. A subclutter 
visibility of, for example, 30 db implies that a moving target can be detected in the 
presence of clutter even though the clutter echo power is 1 ,000 times the target echo 
power. Although the subclutter visibility is widely used as a measure of MTI radar 
performance, caution should be exercised in applying it to describe the relative perform- 
ance of two different MTI radars. Two radars with the same subclutter visibility 
might not have the same ability to detect targets in clutter if the resolution cell of one 
(pulse width times beamwidth) is greater than the other and accepts a greater clutter 



Sec. 4.3] MTI and Pulse-doppler Radar 141 

signal power; that is, both radars might reduce the clutter power equally, but one starts 
with greater clutter power because its resolution cell "sees" more clutter targets. 

The cancellation ratio is sometimes used to describe the performance of the delay-line- 
canceler network. It may be denned as the ratio of a fixed-target signal voltage after 
MTI cancellation to the voltage of the same target without MTI cancellation. The 
cancellation ratio is a number less than 1. Both the subclutter visibility and the 
cancellation ratio are usually expressed in decibels. 

The target-visibility factor, which was mentioned earlier in this chapter (Fig. 4.1 1), is 
defined as the ratio of the (voltage) signal strength from a target traveling at a specified 
radial velocity to the signal strength from the same target when it is traveling at an 
optimum radial velocity. The target-visibility factor applies only when the target is 
not in clutter. 

Equipment Stability. The effect of equipment stability on MTI performance depends 
upon the particular configuration of the radar. For purposes of discussion, the MTI 
radar considered in this section is that illustrated by the block diagram of Fig. 4.6, unless 
otherwise noted. It is a common type of MTI radar and consists of a pulsed oscillator 
transmitter, such as the magnetron, and a delay-line canceler to extract the doppler 
information from moving targets. The performance of MTI radar will deteriorate if 
the transmitter, the stalo, or the echo drift in frequency; if the time delay in the delay 
line does not equal the pulse-repetition interval ; if there are variations in pulse width or 
pulse amplitude; or if the transmitter frequency changes during the pulse. It is also 
possible for the MTI performance to degrade because of such seemingly unimportant 
things as vibrations caused by the blowers used to cool the stalo. 22 

Oscillator Stability. A change in either the transmitter, stalo, or coho frequencies 
will result in an uncanceled residue from fixed targets at the output of the delay-line 
canceler. If the transmitted angular frequency at the time a particular pulse is trans- 
mitted is w t and the phase is 4> t , the transmitted signal may be written as 

Transmitted signal = V t sin (to t t + </>,) (4.31) 

The echo signal from a. fixed target at range R arrives back at the radar receiver a time 
T = 2R/c after transmission. The stalo frequency at the time the echo is received is 
w s , and the IF echo signal at the input to the phase detector is 

IF echo signal = K IF sin [(a> t — co s )t — co t T + <f> t — <f> s ] (4.32) 

where <f> s is the phase of the stalo. It will be recalled that in the MTI which uses an 
oscillator as the transmitter (Fig. 4.6), a portion of the transmitted power provides the 
reference, or locking, pulse which locks the phase of the coho to that of the transmitter. 
The coho signal at time of phase lock is of frequency co c0 , but with phase <f> t — <j> s , and is 
given by 

Coho signal at time of phase lock = V c sin ((o CQ t + <f) t — ff> s ) (4.33) 

During the time T , when the pulse travels to the target and back, the coho oscillator 
might drift in frequency from its initial value to a value co c . Therefore the coho signal 
which is fed to the phase detector at the time of the first echo pulse is 

Coho signal to phase detector = V c sin (a> c t + <f>t — <t>s) (4.34) 

The output of the phase detector is a sine wave with argument equal to the difference 
in the arguments of Eqs. (4.32) and (4.34). Therefore 

Phase-detector output for pulse 1 = k sin [(co t — m s — w c )t — a> t T ] (4.35) 

In a perfect system, (o t = w s + (o c and the phase-detector output is a signal of constant 
amplitude sin co f T . On the succeeding pulse a time Hater, the frequencies of each of 



142 Introduction to Radar Systems [Sec. 4.3 

the oscillators are assumed to have changed, so that the ouput from the phase detector 
may be written as 

Phase-detector output for pulse 2 = k sin [(co' t — w' s — co' c )(t + T) — co' t T^\ (4.36) 

where the primes denote the shifted values of oscillator frequencies. If the change in 
transmitter, stalo, and coho frequencies from one pulse period to the next is denoted 
by Acoj, Acy s , and Aco c , respectively, then a>' t = w t + Aco t , a>' s = a> s + Aco s , and 
(o' c — <t) c + A(o c . The difference between the transmitter and stalo angular frequencies 
is the IF angular frequency, co IF = co t — w s . It will be assumed that the coho frequency 
is not exactly tuned to the intermediate frequency. The difference will be denoted 
Aco IF = a> t — w s — co c . 

The output of the delay-line canceler is the difference between Eqs. (4.35) and (4.36). 
If the oscillator frequencies are not the same from pulse to pulse, a stationary target will 
produce a nonzero output equal to 

Output of delay-line canceler = k sin (Aw IF / — co^o) 

— k sin [(A« IF + Aeoj — Aw s - Aco c )(t + T) — (co t + Aco t )T ] (4.37) 

Equation (4.37) is averaged over the pulse width r from t = T to t = T + r and 
divided by k, to give the cancellation ratio (CR): 

I CTo + r 1 fT + r 

CR = - sin (Aco IF ( — m t T ) dt sin [Aw (r + T) — (m t + Aa> t )T„] < 

tJTo tJt . 

(4.38) 
Performing the integrations and a little 



\dt 



where Aco = Aw IF + Aco t — Aco s — Aw,,, 
trigonometry, the cancellation ratio becomes 



CR = 



2 sin i 



X cos J 



"iF^o + y +A Wo (t 



^) + Aco.To 



+ T + 



l) - Aco t T Q - 



2co t T 



(4.39) 



The absolute value is taken since it is assumed that a full-wave rectifier follows the 
delay-line canceler. In arriving at the above expression it was assumed that 
sin (Aco t/2) (** Aco t/2 and sin (Aco if t/2) s=a Aco if t/2, which are good assumptions 
for most radar applications. For small errors, the argument of the sine factor in Eq. 
(4.39) is also a small quantity, and it is likewise assumed that the sine may be replaced by 
its argument. Although the argument of the sine factor is small, the argument of the 
cosine factor can be a relatively large quantity because the term 2co t T is large. There- 
fore the absolute value of the cosine factor can take on any value from to 1 , depending 
upon the value of T . Its average value is 2/7T. Replacing the rapidly varying cosine 
term by its average value gives the following: 



CR = 



= 4 



Aco if (t + y - A Wo (r +T+^j + Aco t T 

(A/. + a/ c )(t + T+ i) - a/«(t+ ^) - 



A/i F T 



(4.40) 



where 2-nf = co. In most cases the pulse width is small compared with the pulse period 
and t/2 may be neglected with respect to T. For purposes of illustration, take T equal 
to its average value T/2. The cancellation ratio is 



CR = 4 |1.5(A/, + A/ c ) - A/ 4 - A/ IF | T 



(4.41) 



Sec. 4.3] MTI and Pulse-doppler Radar 143 

If all frequency drifts are zero except the stalo, the cancellation ratio is equal to 6 A/ s r. 
If, for example, the cancellation ratio were required to be —40 db and if the pulse 
repetition frequency were 1,000 cps (T = 10~ 3 sec), the stalo frequency shift from pulse 
to pulse must be less than 1.66 cps. For CR = — 30 db, the drift must be less than 
5 cps pulse to pulse and less than 17 cps for a — 20-db ratio. Similar considerations 
apply to the coho frequency drift. Short-term stability of a commercial S-band stalo 
might be of the order of 7 to 10 cps, while the stability of an Z,-band stalo might be 4 to 
8 cps. 23-24 The stability could be improved if desired, but with more sophisticated 
equipment than a simple stalo oscillator. The stability of the coho will be better than 
that of the stalo since it operates at a much lower frequency, usually at 30 or 60 Mc. 

From Eq. (4.41) it is seen that if the only frequency drift is that of the transmitter, 
the residue is equal to 4 &f t T. If there were no frequency drifts in the oscillators, but 
if the coho were mistuned, the cancellation ratio would be 4 A/" IF r. 

The combined effect of frequency drifts in transmitter, stalo, coho, and a mistuned 
coho frequency is difficult to predict because the terms of Eq. (4.41) are not all of the 
same sign and the direction of the frequency drift can be either positive or negative. If 
it is assumed that the drifts follow a Gaussian distribution about some mean value and 
if the standard deviations are designated a t , where i stands for s, c, t, or IF, then the 
rms cancellation ratio may be given by 

CR rms = [(6<r s ) 2 + (6er c ) 2 + (4a t f + (4cr IP ) 2 ]ir (4.42) 

A similar analysis of the stability requirements for the MTI using a power amplifier 
(Fig. 4.5) leads to an interesting result for the case of uniform frequency drifts. Only 
two oscillators are involved, the stalo and the coho. The transmitted frequency is 
assumed to be the sum of the two. It is further assumed that the power amplifier has 
negligible effect on the phase of the transmitted signal. The transmitted signal 
(neglecting amplitude factors) is 

V t = sin [(eo, + w c )t + <f> s + <f> e ] (4.43) 

The received RF signal from a target at a distance R = cT /2 is 

V r = sin [(a,. + a>X* ~ W + & + <f>c\ (4-44) 

On reception the stalo and coho frequencies are assumed to have drifted to new values 
m' s and a>' c . The IF signal is 

K IF = sin [(co s + w e )(t ~ To) - a>',t + <£ c ] (4.45) 

The coho signal on reception is 

V c = sin («# + 4> c ) (4.46) 

Hence the output of the phase detector for the first echo pulse is the difference signal 
obtained by heterodyning Eqs. (4.45) and (4.46) and is 

Pi = k sin [(co s - w',)t + (co c - m' c )t - (ca s + m^T^ (4.47) 

The output of the phase detector for the next pulse, a time T later, may be written 

V 2 = k sin [Ki - <)(t + T) + («j el - (o' cl )(t + T) - {w A + fl> eI )r ] (4.48) 

where a> sl and w cl = stalo and coho frequencies on transmission of second pulse 
m' sl and <x>' cl = stalo and coho frequencies on reception of second pulse 
k = a constant 



144 Introduction to Radar Systems [Sec. 4.3 

If it is assumed that the stalo and the coho drift at a uniform rate Am J At and Am J At, 
then it is seen that 



0) s — 


, Aco s 


m c - 


Am c 


w,l - 


Aft> S7 , 
ffl, = — T — T 
s At 


ft>cl- 


o). = —7 — T 
c At 



and 

The output of the delay-line canceler is V 2 — V ± , or 

* si - »(£ ^ + £ r - r - £ "■• - £ "■■) - [£ *(' + D 

Thus a uniform frequency drift seems to result in perfect cancellation for the power 
amplifier MTI. 

In practice, the drift may not be uniform and the phase variation introduced by the 
amplifier, although small, may not always be neglected. Nevertheless, the above 
crude analysis indicates a possible advantage of the power amplifier MTI as compared 
with the power oscillator MTI. 

Accuracy of Delay Time andPRF. If the delay time and the pulse-repetition period 
are not exactly equal, an uncanceled residue will result from the output of the delay-line 
canceler. The output of the phase detector for a fixed target (f d = 0) is, from Eq. (4.3), 

V = kF(t) sin 4 ^^ 
c 

F(t) = l c c (4-50) 

1,0 otherwise 
where k = a constant 

F{t) = shape of echo signal (assumed rectangular) 
R = range 

f t = transmitted frequency 
c = velocity of propagation 
F(t) is assumed to be a pulse of constant amplitude and of width t. If the difference 
between the prf and the delay time is At, the output of the delay-line canceler will be 

V = k[F(t + At) - F(()] sin^^ (4.5i) 

c 

The average of F(t + At) — F(t) over a time interval t + At is 2 At jr. The average 
cancellation ratio is the average value of V divided by the amplitude of the input signal 
k sin (ATrR f f jc), or 

CR = — (4.52) 

T 



Sec. 4.3] 



MTI AND PULSE-DOPPLER RADAR 145 



For example, if the pulse width were 1 ^sec, the difference between the prf and the 
delay time, At, must be less than 0.005 /^sec for a cancellation ratio of —40 db, 0.015 
^sec for —30 db, and 0.05 ^sec for —20 db. The temperature coefficient for fused 
quartz is approximately 10~ 4 part per degree centigrade at a frequency of 10 Mc and a 
temperature of 20°C. Therefore the temperature of a 1,000-^sec delay line must not 
fluctuate more than 0.05°C if a — 40-db cancellation ratio is to be achieved. Likewise 
the stability of the oscillator which generates the prf must be held to within 1 part in 
2 x 10 5 to obtain a —40-db cancellation ratio. 

A similar derivation can be made to determine the tolerance permitted in the pulse 
width. Although rectangular pulse shapes were assumed, it can be shown that the 
residue area is independent of the pulse shape and depends only upon the maximum 
amplitude of the pulse. 7 





Fig. 4.36. Radar resolution cell (in angle and 
range) and clutter model consisting of many 
independent scatterers randomly distributed. 



Fig. 4.37. Vector summation of the contributions 
from the many independent scatterers con- 
stituting the clutter. 



Internal Fluctuation of Clutter. ib Although clutter targets such as buildings, water 
towers, bare hills, or mountains produce echo signals that are constant in both phase 
and amplitude as a function of time, there are many types of clutter that cannot be 
considered as absolutely stationary. Echoes from trees, vegetation, sea, rain, and 
chaff fluctuate with time, and these fluctuations can limit the performance of MTI 
radar. 

Because of its varied nature, it is difficult to describe precisely the clutter echo signal. 
However, for purposes of analysis, most fluctuating clutter targets may be represented 
by a model consisting of many independent scatterers located within the resolution cell 
of the radar (Fig. 4.36). The echo at the radar receiver is the vector sum of the echo 
signals received from each of the individual scatterers (Fig. 4.37); that is, the relative 
phase as well as the amplitude from each scatterer influences the resultant composite 
signal. If the individual scatterers remain fixed from pulse to pulse, the resultant echo 
signal will also remain fixed. But any motion of the scatterers relative to the radar will 
result in different phase relationships at the radar receiver. Hence the phase and 
amplitude of the new resultant echo signal will differ pulse to pulse. If it can be 
assumed that the relative phases of the echo signals received from the individual 
scatterers are random, that the number of individual scatterers making up the composite 
clutter signal is large, and that the radar cross section of any individual scatterer is 



146 Introduction to Radar Systems [Sec. 4.3 

small compared with the total cross section, then the probability-density function for 
the envelope of the fluctuating echo signal may be represented by Rayleigh statistics. 

The Rayleigh probability-density func- 
tion p{w) for the fluctuations in the 
clutter echo power w is 

p(w) = — exp (- — ) w > (4.53) 

where w is the average power. 

In addition to the fluctuating com- 
ponent of the clutter echo signal, there 
is usually a constant (d-c) component 
about which the fluctuations take 
place. An example might be trees on 
the side of a mountain. The echo 
from the mountain constitutes the con- 
stant portion, while the echo from 
the trees contributes the fluctuating 
portion. The probability distribution 
function for a target which can be rep- 
resented as one large reflector together 
with other small reflectors is 26 



I.U 

0.5 




■f-^l 


! 


1 
\4 


1 


0.2 










\ - 


~ 0.1 




A 


\ 5 




- 


0.05 


2 


i 






- 


0.02 










- 


0.01 




i i 


1 ' 


1 \ 


1 



10 15 
Frequency, cps 



20 



25 



Fig. 4.38. Power spectra of various clutter targets. 
(1) Heavily wooded hills, 20-mph wind blowing 
(a = 2.3 x 10"); (2) sparsely wooded hills, calm 
day (a = 3.9 x 10 1 "); (3) sea echo, windy day 
(a =-- 1.41 x 10 16 ); (4) rain clouds (a = 2.8 x 10 13 ); 
(5) chaff (a = 1 x 10 16 ). (From Barlow, 27 Proc. 
IRE.) 



4w 
— i ex P 



2vv 



P(w) = — exp J ) w > 

(4.54) 

Another property of clutter which 
distinguishes it from normal radar 
targets is that clutter is usually a dis- 
tributed target while aircraft are 
more normally point targets. Further 
discussion of the properties of clutter will be found in Chap. 12. 

Examples of the power spectra of typical clutter are shown in Fig. 4.38. These data 27 
apply at a frequency of 1,000 Mc. The experimentally measured power spectra of 
clutter signals may be approximated by 



W(f) = \g(f)\ 2 = |g | 2 exp 



[-({)*] 



(4.55) 



where W(f) = clutter-power spectrum as a function of frequency 
gif) = Fourier transform of input waveform (clutter echo) 
f = radar carrier frequency 
a = a parameter dependent upon clutter 
Values of the parameter a which correspond to the clutter spectra in Fig. 4.38 are 
given in the caption. 

Clutter fluctuations give rise to an uncanceled output from the delay-line canceler 
which may be calculated in a manner similar to that described for equipment fluctua- 
tions. The difference between the delayed and the undelayed waveforms is averaged, 
and the average power of the residue is a measure of the degree to which the clutter 
signal is attenuated by the delay-line canceler. This is called the clutter attenuation 
(abbreviated CA). Since the time waveform and the frequency spectrum are related by 



Sec. 4.3] MTI and Pulse-doppler Radar 147 

the Fourier transform, it is also possible to compute the clutter attenuation using 
the frequency spectrum instead of the time waveform. 

The delay-line canceler was shown in its barest essentials in Fig. 4.4. The frequency- 
response function of the delay line is exp (—j(o/f r ), where f r is the pulse repetition 
frequency and is equal to the reciprocal of the time delay of the line. The frequency- 
response function of the delay-line canceler is therefore 

H(f) = 1 - exp (- &\ = 2/ sin ^exp (- j ^-\ (4.56) 

* Jr Jr ^ Jr ' 

The Fourier transform of the input waveform g x (f), when multiplied by the frequency- 
response function of the delay-line canceler, yields the Fourier transform of the output 
waveform g 2 (f). 

gzif) = gi(f)H(f) (4-57) 

The attenuation of the clutter signal by the delay-line canceler (clutter attenuation, 
abbreviated CA) may be written as the ratio of the input power divided by the output 
power : 

\gi(f)?df \ gl (f)\ 2 df 
CA = T^ = -J^ (4-58) 

\g2(f)\ 2 df 4 \ gl (f)\* sin* (nf/f r )df 

Jo Jo 

Substituting Eq. (4.55) for the input g x (f) into the above gives 



CA 



f°° exp [-«(///„)*] df 
Jo 

4 f °° sin 2 (*///,) exp [-a(/// ) a ] df 

Jo 



Integrating, the clutter attenuation may be written as 

CA = ^ — (4.59) 

1 _ exp [-(nfJfM 

Equation (4.59) is plotted in Fig. 4.39 28 for several values of the ratio f /f r and as a 
function of the parameter a. Also indicated on the figure are the values of a which 
correspond to the experimental data of Fig. 4.38. If the exponent in the denominator 
of Eq. (4.59) is small compared with unity, the exponential term can be replaced by the 
first two terms of a series expansion with little loss of accuracy, or 

CA *» — - (4.60) 

Wolf? 

Equation (4.59) was derived for a single-delay-line canceler. The equivalent 
expression for the clutter attenuation provided by a double-delay-line canceler is 29 

CA = — (4.61) 

3 - 4 exp [-(77/ // r ) 2 /a] + exp [-4( 7 ,/ // r ) 2 /«] 

For (nf lf r yia< 1, 

CA ^ (4.62) 

12^/o/X) 4 

The frequency dependence of the clutter spectrum as given by Eqs. (4.59) and (4.61) 
cannot be extended over too great a frequency range since the derivation does not take 



148 



Introduction to Radar Systems 



[Sec. 4.3 



into account any variation of cross section of the individual scatterers as a function of 
frequency. The leaves and branches of trees, for example, may have considerably 
different reflecting properties at a wavelength of 1 cm, where the dimensions are 
comparable with the wavelength, from those at a wavelength of, say, 50 cm, which is 
long compared with the dimensions. 




10 



10' 



10' 7 10' 8 

Clutter spectrum exponent a. 



to'' 



to 20 



Fig. 4.39. Effect of internal fluctuations on clutter attenuation. (From Grisetti et al., 2S IRE. Trans.) 



Scanning Fluctuations. Assume, as before, the clutter echo to be the vector sum of 
the echoes from a number of independent scatterers included within the radar resolution 
cell. Even if all the individual scatterers were fixed so that there were no internal 
clutter motion, an uncanceled residue would result at the output of the delay- line 
canceler if the antenna is in motion. Antenna motion may be due to a rotation and/or 
a translational movement of the radar platform. Only the fluctuations in the echo 
caused by the rotational scanning of the antenna (scanning fluctuations) will be con- 
sidered here. Fluctuations caused by motion of the radar platform are not present in a 
fixed, ground-based radar. They are of importance, however, in a radar carried on 
board a moving vehicle and will be considered later in Sec. 4.8. 

Assuming the usual idealized clutter target, the echo signal will consist of the vector 
sum of the contributions from the many independent scatterers randomly distributed 
within the radar resolution cell. Because the scatterers are considered to be independ- 
ent, the received echo power is equal to the sum of the average power scattered by each 
of the objects. The power received from a stationary, distributed clutter target will be 
proportional to 



J 



G 2 (0) dd 



(4.63) 



where G(6) is the one-way antenna power gain as a function of the angle 8 (two-way 
voltage gain). The gain enters as the square in Eq. (4.63) because of the two-way 
transit of radar signals. It is further assumed in this analysis that the antenna elevation 
angle is zero. 



Sec. 4.3] MTI and Pulse-doppler Radar 149 

The scanning motion of the antenna causes the beam to shift to a slightly different 
azimuth on each pulse. Most scatterers remain within the beam. Some scatterers, 
however, are no longer illuminated, while others enter the beam and become illuminated. 
The result is that the total number of illuminated scatterers will be essentially the same 
from pulse to pulse but their relative distribution in space and their relative phase 
relations will be different. The resultant echo-signal voltage therefore varies from 
pulse to pulse, and an uncanceled residue remains at the output of the delay-line 
canceler. The uncanceled residue from two successive pulses is proportional to 



/: 



[G(0 + A0) - G(0)] 2 dd (4.64) 

where A0 is the angular motion of the antenna between pulses . The clutter attenuation 
is then 

f 00 /*0O 

G\6)d6 G 2 (6)d6 

CA = 7^ — ~ ~^t ( 4 - 65 ) 

[G(0 + A0) - G(0)] 2 dd (A0) 2 [G'(6)fde 

J — oo J — 00 

In the above the voltage difference G(6 + Afl) — G(d) was replaced by G'(0) A0, which 
follows from the definition of the derivative when A0 is small. Strictly speaking, the 
limits of integration do not extend from — oo to + oo since the angle does not extend 
beyond 2-n- radians. In fact, the angular region of interest is only that region in the 
vicinity of the main beam. The limits in Eq. (4.65) were chosen, however, for ease of 
integration. Integration over the entire range of values does not appreciably affect the 
final result if narrow beamwidths and reasonably low antenna sidelobe levels are 
assumed. The antenna pattern is assumed to be of Gaussian shape 



,v/,x ~ / 2.7760 2 \ 
(7(0) = G exp ^ gg-j 



where is measured from the axis of the beam, B is the beamwidth included within the 
half-power points of the antenna pattern, and G is the maximum antenna gain. Sub- 
stituting this into Eq. (4.65) and evaluating the integrals gives 

CA = -2S- (4.66) 

2.776 

where n B = 0#/A0 is the number of hits included within the 3-db beamwidth B . 
There is very little difference in the results if instead of a Gaussian antenna pattern, a 
pattern of the form (sin 0)/0 is chosen. 28 

The residue left after cancellation may be divided into an amplitude component and a 
phase component. Let R be the rms value of the signal voltage R, and let r be the rms 
value of the voltage residue r which remains after cancellation. The clutter attenuation 
of Eq. (4.65) is then Rl/r^. The vector r can be resolved into two components, one in 
the direction of R, the other at the right angles to R. The rms value of each of these 
two components is rjVl. Thus the rms amplitude fluctuation of the residue is r /V2, 
while the rms phase fluctuation is approximately r /(R V2), if R > r . Therefore, 
if an amplitude detector is used (as in the noncoherent radar described in Sec. 4.6), the 
phase fluctuations are eliminated, leaving only the amplitude fluctuations. The clutter 
attenuation in this case is twice that of Eq. (4.66). If the amplitude fluctuations are 
eliminated with a limiter, only the phase fluctuations remain. By converting phase 



150 



Introduction to Radar Systems 



[Sec. 4.3 

fluctuations to amplitude fluctuations with the phase detector (as in the coherent MTI), 
the clutter attenuation is twice that of Eq. (4.66), or 



CA 



1.388 



(4.67) 



A plot of this equation is shown in Fig. 4.40. 

The clutter attenuation may be improved by passing the output of the delay-line 
canceler through a second delay-line canceler (double cancellation). The output of 



70 

60 

-q50 

C 

o 

140 

3 
C 
<D 

°30 

o20 

10 






' I i I I i il 



J I I I I l I I 



I I I II II 



2 5 10 20 50 100 200 500 1,000 

rig, number of hits included within 3 db beamwidth 



Fig. 4.40. Clutter attenuation with a scanning antenna for single cancellation and double cancellation. 
Antenna pattern assumed to be of Gaussian shape. 

the second canceler is [G'(6 + A0) - G'(6)] A0 & G"(6)(A6f, which results in the 
following: 



CA 



r 



G 2 (0) dd 



(A0) 4 \ [G"(d)J dd 

J — CO 



(4.68) 



If either an amplitude or a phase detector is employed in the receiver, the clutter 
attenuation will be twice this value, just as with single cancellation. For a Gaussian 
beam shape the clutter attenuation is k^/11.5. This is also plotted in Fig. 4.40. 

Antenna scanning fluctuations may be eliminated by holding the beam stationary at 
each angular sector for a period of time sufficient to obtain the number of pulses 
required for detection. The antenna is then shifted rapidly to the next angular position, 
where it again remains stationary during the observation time. This is called step 
scanning. 

Another technique for reducing the effects of scanning is based on radiating an 
antenna pattern which maximizes the clutter attenuation. 28 - 30 If an antenna pattern 
proportional to G'(6) is added to the normal antenna pattern G(6) before cancellation 
with G(6 + A0), the residue will be considerably reduced. The denominator of Eq. 
(4.65) will be small (ideally zero), and thus the clutter attenuation will be large. Since 
the usual antenna pattern G(0) is an even function of 0, the derivative pattern G'(d) will 
be an odd function. Even and odd antenna patterns may be obtained with two-feed 



Sec. 4.4] MTI and Pulse-doppler Radar 151 

antennas and proper RF combining circuitry, as in simultaneous lobing or monopulse 
antennas. The two feeds are displaced from the antenna axis to produce two adjacent 
beams. The sum of the two gives an even pattern; their difference, an odd pattern. 
Proper combination of the even and odd antenna patterns stabilizes the far-field 
amplitude and phase radiation patterns in space, independent of the antenna motion. 
Complete stabilization of the radiation patterns during the cancellation periods 
eliminates the residue caused by scanning. 

4.4. MTI Using Range Gates and Filters 

In the previous discussion, the MTI radar was assumed to use a delay-line canceler as 
the filter which rejects clutter echoes and passes only those doppler-frequency-shifted 
signals returned from moving targets. In this section a different filtering technique for 
rejecting clutter echoes will be described. The video clutter spectrum, as was seen in 
Fig. 4.38, is spread over a finite frequency range. The shape and magnitude of the 
frequency spectrum depend upon several factors, including the nature of the clutter 
illuminated by the radar beam, the antenna scanning, and the equipment stability. In a 
pulse radar the clutter spectrum is reflected about each of the spectral lines (Fig. 4.22) 
located at the pulse repetition frequency and its harmonics. This effect is known as 
clutter foldover. 

The ideal-filter characteristic would reject the maximum amount of clutter energy 
without significantly rejecting any doppler signals which fall outside the clutter spec- 
trum. The ideal filter is the matched filter (Sec. 9.2), which maximizes the signal-to- 
noise ratio at the output. Unfortunately, the matched filter is sometimes difficult to 
synthesize and some practical compromise must usually be made. 

The delay-line canceler is one form of filter used to approach the matched-filter 
characteristic. The single-delay-line canceler is a poor approximation to the ideal 
filter, but it has the advantage of simplicity. Double cancellation is somewhat better 
than the single delay line, but it still leaves much to be desired. Delay-line cancelers are 
not limited to sin x or sin 2 x characteristics. They may be designed to have a wide 
variety of frequency characteristics as described in a previous section. Hence only 
economic or space considerations limit the degree to which the delay-line canceler can 
be made to approach the ideal matched filter. An advantage of the delay-line canceler 
as a filter is that range information is preserved in the output. Its chief limitations are 
the additional complexity required to achieve special filter characteristics and the need 
for maintaining perfect adjustment in the delay lines if the theoretical performance is to 
be achieved in practice. 

Although a simple narrowband filter might be used in an MTI radar to pass the 
doppler-frequency components of moving targets and reject the direct current due to 
clutter, it suffers from two major limitations. A narrowband filter destroys the range 
resolution in an ordinary system because the duration of its impulse response is approxi- 
mately the reciprocal of the bandwidth. Furthermore, the signal-to-noise ratio is 
reduced when narrowband filters are used without range gating because of the collapsing 
loss (Sec. 2.12). The collapsing loss is caused by additional noise that enters the filter 
from the other range intervals which do not contain the target signal. The loss of the 
range information and the collapsing loss may be eliminated by first quantizing the 
range (time) into small intervals. This process is called range gating. The width of 
the range gates depends upon the range accuracy desired and the complexity which can 
be tolerated, but they are usually of the order of the pulse width. Range resolution is 
established by gating. Once the radar return is quantized into range intervals, the 
output from each gate may be applied to a narrowband filter since the pulse shape need 
no longer be preserved for range resolution. A collapsing loss does not take place 
since noise from the other range intervals is excluded. 



152 Introduction to Radar Systems [Sec. 4.4 

A block diagram of the video of an MTI radar with multiple range gates followed by 
clutter-rejection niters is shown in Fig. 4.41. The output of the phase detector is 
sampled sequentially by the range gates. Each range gate opens in sequence just long 
enough to sample the voltage of the video waveform corresponding to a different range 
interval in space. The range gate acts as a switch or a gate which opens and closes at 
the proper time. The range gates are activated once each pulse-repetition interval. 
The output for a stationary target is a series of pulses of constant amplitude. An echo 
from a moving target produces a series of pulses which vary in amplitude according to 



Phase 
detector 



Range 
gate 
No. t 



Boxcar 
generator 



Bandpass 

(Ooppler) 

filter 


> - 


Full-wave 

linear 
defector 


-> — 


Low pass 

filter 
(integrator) 



Threshold -*■ 



Range 
gate 
No. 2 


— 


Boxcar 
generator 


-> — 





Threshold 



Range 
gate 

No. 3 



" To dato 
" processing 
„ or display 



(Range 
L ->-j gate -*— 
[No.n 



Boxcar 
generator 



Threshold 



Fig. 4.41. Block diagram of MTI radar using range gates and filters. 

the doppler frequency. The output of the range gates is stretched in a circuit called the 
boxcar generator, whose purpose is to aid in the filtering and detection process by 
emphasizing the fundamental of the modulation frequency and eliminating harmonics 
of the pulse repetition frequency (Sec. 5.3). The clutter-rejection filter is a bandpass 
filter whose bandwidth depends upon the extent of the clutter spectrum but is less than 
fj2, where f r is the pulse repetition frequency. The doppler filters utilize lumped- 
constant circuit elements. The lower cutoff frequency can be designed to be adjusted 
to different values, depending on the characteristics of the clutter spectrum. 



-go 



£=Vr 



Frequency 



Zfr 



3/, 



Fig. 4.42. Frequency-response characteristic of an MTI using range gates and filters. 

Following the doppler filter is a full-wave linear detector and an integrator (a low- 
pass filter). The purpose of the detector is to convert the bipolar video to unipolar 
video. The output of the integrator is applied to a threshold-detection circuit. Only 
those signals which cross the threshold are reported as targets. Following the threshold 
detector, the outputs from each of the range channels must be properly combined for 
display on the PPI or A-scope or for any other appropriate indicating or data-processing 
device. The CRT display from this type of MTI radar appears "cleaner" than the 
display from a normal MTI radar, not only because of better clutter rejection, but also 
because the threshold device eliminates many of the unwanted false alarms due to 
noise. The frequency-response characteristic of the range-gated MTI might appear as 
in Fig. 4.42. The shape of the rejection band is determined primarily by the shape of 
the bandpass filter of Fig. 4.41. 



Sec. 4.5] MTI AND Pulse-doppler Radar 153 

MTI radar using range gates and niters is usually more complex than an MTI with a 
single-delay-line canceler. The additional complexity is justified in those applications 
where good MTI performance and the flexibility of the range gates and filter MTI are 
desired . The better MTI performance results not only from the better match between 
the clutter filter characteristic and the clutter spectrum, but also because limitations 
peculiar to the delay-line canceler, such as maintaining the time delay constant in spite 
of temperature changes, are not present. 

4.5. Pulse-doppler Radar 31 ~ 33 

The pulse-doppler radar is a form of MTI radar usually, but not necessarily, charac- 
terized by one or more of the following: 

1. A series of range gates and doppler rejection niters rather than the delay-line 

2. A klystron amplifier transmitter rather than a magnetron oscillator 

3. A relatively high pulse repetition frequency with ambiguous range but unambigu- 
ous doppler (no blind speeds within expected range of doppler frequencies) 

The above is not meant to define a pulse-doppler radar, nor should it be implied that a 
radar with any one of these characteristics is necessarily a pulse-doppler radar. A 
precise distinction between the MTI and the pulse-doppler radars does not seem to be 
generally agreed upon. However, for purposes of this text, a pulse-doppler radar will 
usually be assumed to be characterized by the above attributes. These characteristics 
usually result in better MTI performance (better subclutter visibility) than is possible 
with the type of MTI radar considered previously, that is, one which uses a delay-line 
canceler and which has many blind speeds within the expected range of doppler fre- 
quencies. 

The pulse-doppler radar, when operating with high prf's to avoid doppler blind 
speeds, may have to accept ambiguous range information. The presence of range 
ambiguities not only confuses the knowledge of target range, but also creates intervals 
where the target will not be detected. These are called blind ranges and occur when the 
transmitter is turned on and the receiver is turned off. If both the doppler and the 
range are ambiguous, there will exist both blind ranges and blind speeds, which further 
reduce the coverage of the radar. The effect of blind ranges can be alleviated, and the 
range ambiguities can be resolved by transmitting at more than one prf. 

When the prf must be so high that the number of range ambiguities is too large to be 
easily resolved, the performance of the pulse-doppler radar approaches that of the CW 
doppler radar. The pulse-doppler radar, like the CW radar, may be limited in its 
ability to measure range under these conditions. Even so, the pulse-doppler radar has 
an advantage over the CW radar in that the detection performance is not limited by 
transmitter leakage or by signals reflected from nearby clutter or from the radome. 
The pulse-doppler radar avoids this difficulty since its receiver is turned off during 
transmission, whereas the CW radar receiver is always on. On the other hand, the 
detection capability of the pulse-doppler radar is reduced because of the blind spots in 
range resulting from the high prf. Pulse-doppler-radar equipment will usually be 
more complex than that of CW radar, except that a CW radar will often use two 
separate antennas for transmit and receive while the pulse doppler can operate with a 
single antenna. Neither the CW nor the pulse-doppler radar seems to have a clear-cut 
advantage over the other in those applications where range information is not obtained, 
as, for example, in a homing missile. 

One other method should be mentioned of achieving coherent MTI. If the number 
of cycles of the doppler frequency shift contained within the duration of a single pulse is 
sufficient, the returned echoes from moving targets may be separated from clutter by 
suitable RF or IF filters. This is possible if the doppler frequency shift is at least 



} 



TR 



Power 
oscillator 



Modulator 



Mixer 



LO 



IF 
amplifier 



Amplitude 
defector 



t; 



154 Introduction to Radar Systems [Sec. 4.6 

comparable with or greater than the spectral width of the transmitted signal. It is not 
usually applicable to aircraft targets, but it can sometimes be applied to radars designed 
to detect extraterrestrial targets such as satellites or astronomical bodies (Chap. 14). 
In these cases, the transmitted pulse width is relatively wide and its spectrum is narrow. 
The high speed of extraterrestrial targets results in doppler shifts that are usually 
significantly greater than the spectral width of the transmitted signal. 

4.6. Noncoherent MTI 

The composite echo signal from a moving target and clutter fluctuates in both phase 
and amplitude. The coherent MTI and the pulse-doppler radar make use of the phase 
fluctuations in the echo signal to recognize the doppler component produced by a 
moving target. In these systems, amplitude fluctuations are removed by the phase 

detector. The operation of this type of radar, 
which may be called coherent MTI, depends 
upon a reference signal at the radar receiver 
that is coherent with the transmitter signal. 

It is also possible to use the amplitude fluc- 
tuations to recognize the doppler component 
produced by a moving target. MTI radar 
which uses amplitude instead of phase fluc- 
tuations is called noncoherent (Fig. 4.43). It 
has also been called externally coherent. The 
noncoherent MTI radar does not require an 
internal coherent reference signal or a phase 
detector as does the coherent form of MTI. 
Amplitude limiting cannot be employed in the 
noncoherent MTI receiver, else the desired 
amplitude fluctuations would be lost. There- 
fore the IF amplifier must be linear, or if a 
large dynamic range is required, it can be logarithmic. A logarithmic gain charac- 
teristic not only provides protection from saturation, but it also tends to make the 
clutter fluctuations at its output more uniform with variations in the clutter input 
amplitude. The detector following the IF amplifier is a conventional amplitude de- 
tector. The phase detector is not used since phase information is of no interest to the 
noncoherent radar. The local oscillator of the noncoherent radar does not have to be 
as frequency-stable as in the coherent MTI. The transmitter must be sufficiently stable 
over the pulse duration to prevent beats between overlapping ground clutter, but this 
is not as severe a requirement as in the case of coherent radar. The output of the 
amplitude detector is followed by an MTI processor such as a delay-line canceler. 
The doppler component contained in the amplitude fluctuations may also be detected 
by applying the output of the amplitude detector to an A-scope. Amplitude fluctua- 
tions due to doppler produce a butterfly modulation similar to that in Fig. 4.3, but in 
this case, they ride on top of the clutter echoes. Except for the inclusion of means to 
extract the doppler amplitude component, the noncoherent MTI block diagram is 
similar to that of a conventional MTI pulse radar. 

The advantage of the noncoherent MTI is its simplicity; hence it is attractive for those 
applications where space and weight are limited. Its chief limitation is that the target 
must be in the presence of relatively large clutter signals if moving- target detection is to 
take place. Clutter echoes may not always be present over the range at which detection 
is desired. The clutter serves the same function as does the reference signal in the 
coherent MTI. If clutter were not present, the desired targets would not be detected. 
It is possible, however, to provide a switch to disconnect the noncoherent MTI operation 



To cancellation circuits 

Fig. 4.43. Block diagram of a noncoherent 
MTI radar. 



Sec. 4.7] MTI and Pulse-doppler Radar 155 

and revert to normal radar whenever sufficient clutter echoes are not present. If, in a 
noncoherent MTI radar, there is no clutter but there is more than one moving target, the 
target with the lowest doppler frequency can act as the reference signal and detection 
can take place. 

The noncoherent technique is a relatively cheap form of MTI that might be used in 
applications where equipment simplicity is an important consideration and where only 
moderate MTI performance is needed. 

4.7. MTI from a Moving Platform— AMTI 

When the radar itself is in motion, as with a shipboard or airborne radar, the detection 
of a moving target in the presence of clutter is more difficult than if the radar were 
stationary. From the viewpoint of the radar the clutter appears to be in motion, and 
the doppler effect shifts the clutter echo signal just as any other target with the same 
relative velocity. Since the relative velocity between radar and target will usually be 
different from the relative velocity between clutter and radar, the clutter echo may be 
discriminated on the basis of doppler frequency. However, the problem is more 
difficult than with a stationary radar since the relative velocity of the clutter will, in 
general, change with time. In an airborne surveillance radar, for example, the relative 
clutter velocity depends on the aircraft velocity and the direction of the clutter relative 
to the aircraft velocity vector. Since the clutter doppler frequency is not zero with a 
moving radar, the clutter rejection filters must be bandpass rather than low-pass as in 
the stationary case. 

The closer the relative velocity of the clutter to that of the target, the more difficult it 
will be to separate the two. For instance, a radar on board a moving ship will experience 
only slight difficulty (relatively speaking) in separating aircraft targets from sea clutter 
since their doppler frequency shifts will normally be widely separated. On the other 
hand, the converse may not be true. An airborne radar might experience considerable 
difficulty in seeing the ship in the presence of sea clutter, for their doppler frequencies 
may not be too different. The present discussion will be confined to the airborne MTI 
radar (commonly abbreviated AMTI). 

A high-speed fighter aircraft might employ an AMTI radar during the search phase 
of an interception to seek out the hostile target in the presence of clutter. The lower 
the altitude of the target aircraft, the more likely that clutter will be present. Another 
possible military application of AMTI is in long-range search radars installed in high- 
altitude aircraft for the purpose of detecting other aircraft, as the Navy's seaward 
extension of the Early Warning line. The AMTI is of special interest as a radar 
technique, irrespective of its application, since good AMTI performance is not always 
easy to achieve and represents a challenge to the radar designer. 

Coherent AMTI. In principle, any of the MTI techniques that have been discussed 
can be applied to the AMTI radar. However, not all perform equally satisfactorily, 
and in general, it is usually more difficult to achieve a good AMTI radar than it is to 
achieve a good MTI radar. 

The coherent MTI radar which was discussed in a previous section may be applied as 
an AMTI radar if the frequency of the coherent oscillator (coho) is shifted to compensate 
for the relative velocity of the radar platform with respect to the clutter. The block 
diagram of a coherent AMTI radar is shown in Fig. 4.44. It is quite similar to the 
ordinary coherent MTI radar shown in Fig. 4.6 except for the manner in which the coho 
signal is utilized. The output of the coho is mixed with a signal from a tunable oscillator 
called the doppler-frequency oscillator. The frequency of this oscillator is made to be 
proportional to the relative velocity between radar and clutter and may be controlled 
according to the position of the antenna with respect to the clutter. One of the side- 
bands of the heterodyned signals is selected by a narrowband filter and is used instead 



156 Introduction to Radar Systems 



[Sec. 4.7 



of the coho as the reference for the phase detector. This signal is coherent with the 
transmitted signal but is shifted in frequency by an amount sufficient to compensate 
for the relative velocity of clutter. 

As the radar antenna beam scans in angle, the frequency of the doppler-compensation 
oscillator must be correspondingly changed since the relative clutter velocity changes 
with the direction of the antenna beam. Doppler compensation is possible if the 
antenna beamwidth is sufficiently small so that the patch of illuminated clutter returns 
an echo in which the contributions from the various scatterers constituting the clutter 
experience nearly identical doppler frequency shifts. However, when the antenna 
pattern is broad in elevation and the size of the illuminated patch is determined by the 
pulse width rather than the antenna beamwidth, the angle to the clutter will change as 



^ 




TR 






Power 
oscillator 










V 




















' 












i 




















Mixer 




Stalo 




Mixer 














■ 


' 








" 








IF 
amplifier 




Coho 








• 








fc 


V 










Phase 
detector 


f c\U 


Sideband 
filter 


M 


Mixer 


fd 


Doppler 
frequency 
oscillator 






fc-fd 






















\ 

To cancellation 
circuits 







Control 



Fig. 4.44. Block diagram of a coherent AMTI radar. 

the pulse travels out in range. Therefore the effective doppler frequency of the ground 
clutter may vary appreciably over the range interval of interest and make the doppler 
compensation of the coho signal extremely difficult, limiting the usefulness of the 
coherent AMTI in some instances. 

Pulse-doppler AMTI. It was pointed out previously that the pulse-doppler radar is 
capable of good MTI performance; therefore, properly modified, it should also be one 
of the better forms of AMTI radar. The ground-clutter signal, shifted in frequency by 
the doppler effect, may be eliminated by a rejection filter centered at the doppler 
frequency in either the video or the IF. Since the clutter doppler frequency shift 
changes as the antenna scans, a tunable filter must automatically track the changing 
doppler. As in the coherent AMTI, the ability of the pulse-doppler radar to eliminate 
clutter will be limited if the rejection filter cannot continually track the changing 
doppler frequency caused by a changing relative velocity. For this reason narrow 
pencil-beam antennas are preferred to broad fan beams. With a narrow pencil beam, 
changes in doppler occur as the antenna is scanned in angle, but with a broad fan bearn^ 
the doppler may change as the pulse sweeps across the clutter, traveling at the velocity 
of light. If the clutter echo changes in frequency too rapidly, a single broad clutter- 
rejection filter might be used, with a resultant loss in detection capability. 

Noncoherent AMTI. The noncoherent MTI principle can also be applied to a radar 
on a moving platform. It is especially attractive for operation in aircraft, where space 
and weight must be kept to a minimum. The noncoherent AMTI is limited, as was its 



Sec. 4.8] MTI and Pulse-doppler Radar 157 

ground-based counterpart, by the need for sufficient clutter signal to provide the 
reference upon which the doppler fluctuations may be detected. 

4.8. Fluctuations Caused by Platform Motion 30 3436 

In Sec. 4.3, some of the limitations of the MTI radar were discussed, including 
internal fluctuations of the clutter, equipment instabilities, and scanning fluctuations. 
These also limit the performance of the AMTI radar. But in addition, there is another 
serious source of fluctuation in the AMTI radar, caused by motion of the radar platform. 
Fluctuations due to platform motion are quite similar to antenna scanning fluctuations. 
In fact, scanning fluctuations are but a special case of platform motion. 

The patch of clutter which the radar illuminates is assumed to consist of a large 
number of independent scatterers randomly located within the resolution cell of the 
radar. The echo signals from each of these scatterers add vectorially at the radar 
receiving antenna. However, if the radar beam moves between pulses, the distance to 
each of the scatterers changes. A change in distance results in a change in phase, and 
the vector addition of the echo signals from all the scatterers may not be the same from 
pulse to pulse. Not only will the resultant amplitude change from pulse to pulse 
because of relative phase differences between the individual scatterers, but it may differ 
because of the shape of the antenna pattern. Thus the clutter return, instead of being 
constant, will fluctuate from pulse to pulse, and an uncanceled residue will result at the 
output of the delay-line canceler. The uncanceled residue also can be analyzed as a 
spread in the clutter energy spectrum; hence the MTI with range gates and filters will 
likewise be adversely affected by platform motion. 

The clutter attenuation due to radar platform motion has been derived for the 
delay-line canceler by George 34 and Dickey. 35 A more descriptive discussion than 
found in either of these two papers is given in Ridenour (Ref. 1 , sec. 16.13). Urkowitz 36 
extended George's formulas to include terrain that contains a reflector (stationary or 
moving) which has much greater reflectivity than the area around it. Echo fluctuations 
due to the motion of the antenna on board the aircraft may be resolved into four 
components : one component is due to the rotation of the antenna (scanning fluctuation), 
and the other three components are due to the motion of the aircraft in space. Dickey 
derived expressions for these four components of fluctuation, assuming three different 
types of antenna radiation patterns— a rectangular pattern, a Gaussian pattern of the 
form exp (— a 2 2 ), and a pattern of the form (sin 6)16. The three components of 
aircraft motion are defined by a rectangular coordinate system. The z axis is located 
along the center of the antenna beam, and the x axis is horizontal. The y axis is, in 
general, not vertical, but falls in the same vertical plane as the z axis. The approximate 
clutter attenuation for the four components, assuming a Gaussian antenna pattern, aref 

CA for rotation 



1.388 



CA for x axis ~ y88A^_ a 2 

(nvT6 B sin a) 2 1.37(»Tsm a) 2 



CA for y axis 



1.388(Afc) : 



2 



(ttvcTt cos a sin 2 </> tan <f>) 2 

CA for z axis — large enough to be neglected 

t These expressions apply to an MTI receiver sensitive to either the phase component (limiting 
receiver with phase detector) or to the amplitude component (noncoherent MTI), but not to both. 



158 Introduction to Radar Systems 



[Sec. 4.8 



where n B = number of hits per 3-db beamwidth 
6 B = 3-db beamwidth 
X = wavelength 
v = target velocity 
T = pulse-repetition period 

<x = azimuth angle between direction of aircraft motion and projection of 
antenna beam in the horizontal plane (beam points straight ahead at 
a = 0°; beam points perpendicular to aircraft at a = 90°) 
<f> = elevation angle between horizontal plane and center of beam 
t = pulse width 

a = aperture of a uniformly illuminated antenna 
c = velocity of propagation 
These approximate expressions apply when the attenuation is large. More exact 
expressions may be found in Dickey's paper. 35 

The clutter attenuation for rotation is the 
same as that for the scanning fluctuation de- 
rived in Sec. 4.3 for the stationary radar. The 
clutter along the z axis is usually well attenu- 
ated and may be neglected. The total 
fluctuation may be obtained by adding con- 
tributions from each of the four components 
of motion. 

At any particular direction, some of the 
components have greater effect than others. 
Figure 4.45 indicates the regions where each 
component is likely to predominate. The x 
component is important in regions to the 
side. The y component becomes of impor- 
tance along the ground track where the x 
component goes to zero. It is large, however, 
only where the depression angle is large, and 
it is important, therefore, at high altitudes. The scanning component, as was found 
previously, is dependent on the rate of rotation and is independent of the azimuth or 
elevation angle. This component may limit the AMTI performance at long range and 
along the ground track, where the x and y components both become small. At long 
range and along the ground track the z component also may be appreciable. Along 
the ground track, except at extreme range, the pulse length contributes more to the 
fluctuation than the beamwidth, while at right angles to the ground track, the reverse 
is true. Contours of constant clutter attenuation for a particular set of assumed con- 
ditions are shown in Fig. 4.46. Clutter attenuation depends only slightly on the 
antenna pattern. 35 

Figure 4.46 shows that the clutter attenuation (and hence the AMTI performance) 
deteriorates when the antenna beam is perpendicular to the ground track or when the 
beam is pointing directly below the aircraft. Clutter fluctuations are least (greatest 
attenuation) along the ground track at relatively long ranges. The above example 
shows the difficulties involved in attempting to design an AMTI radar with 360° 
scanning coverage. In practice, the problem may be even more formidable than that 
of this example, since aircraft speeds can be considerably higher than the 250 knots 
assumed, and the pulse repetition frequency might be smaller than 2,000 cps, especially 
if a long, unambiguous range were desired. Both a higher aircraft velocity and a lower 




Direction of 

aircraft 

motion 



CA r 



Fig. 4.45. Regions in which each component 
of ground-clutter residue is likely to be 
prominent. (After Dickey, 35 IRE Trans.) 



prf make the AMTI performance worse. 



Sec. 4.9] 



MTI AND PULSE-DOPPLER RADAR 



159 



Direction 
of motion 



\Z <B> 




Fig. 4.46. Typical ground-clutter attenuation for airborne MTI. 
= J /xsec ; prf = 2,000 cps ; ground speed = 250 knots ; altitude 
antenna rotation = 12 rpm. {From Dickey, 3 ' IRE Trans.) 



Beam width = 3.0°; pulse length 
= 20,000 ft; wavelength = 3.2 cm; 



4.9. Effect of Sidelobes on Pulse-doppler AMTI Radar 32 

There will always be undesired sidelobe radiation from an antenna in directions 
other than the main beam. In an airborne radar the troublesome sidelobes are those 
which illuminate the ground. Although the sidelobe radiation may be small compared 
with that from the main beam, the relatively short distance to the ground plus the 
relatively large cross section of the ground at perpendicular incidence (Sec. 12.2) 
combine to give large clutter contributions from the sidelobes. Therefore the moving- 
target signal must compete not only with the clutter illuminated by the main beam, but 
with clutter illuminated by the sidelobes. In this section the effect of the sidelobes on 
the pulse-doppler AMTI radar will be considered qualitatively. Similar considerations 
apply to other types of AMTI radars. 

The spectrum of the transmitted waveform of a pulse radar is depicted in Fig. 4.47. 
It consists of a series of spectral lines separated from one another in frequency by the 
pulse repetition frequency f r . The envelope of the spectral lines follows a (sin x)jx 
shape about the transmitted frequency f . The width of the envelope as measured 
between the first pair of zero crossings aboutyj, is equal to 2/t, where t is the pulse width. 
If both the target and radar were stationary and if there were no clutter echoes, the 
frequency spectrum of the echo signal would be the same as that of the transmitted 
signal. However, the relative motion between radar and target as well as between 



160 



Introduction to Radar Systems 



[Sec. 4.9 

radar and clutter and the additional clutter signal received from the antenna sidelobes 
will substantially modify this idealized signal spectrum. 

The spectrum of the received signal for the pulse AMTI radar might appear as in 
Fig. 4.48. Only that portion of the spectrum in the vicinity of/ is shown. The shape 
of the clutter spectrum about each of the other spectral components spaced at intervals 
equal to the pulse repetition frequency is the same as that about/ . The leakage of the 
transmitter signal into the receiver produces the spike at a frequency^ and the spikes 
at/ ± nf r , where n is an integer and f r is the pulse repetition frequency. Also in the 
vicinity of f is the clutter energy from the sidelobes which illuminate the ground 

-2/r 



M 



Jjillix. 



'o 
Frequency 

Fig. 4.47. Spectrum of pulse-radar transmitted waveform. 

directly beneath the aircraft. The echo from the ground directly beneath the aircraft 
is called the altitude return. The altitude return is not shifted in frequency since the 
relative velocity between radar and ground is essentially zero. Clutter to either 
side of the perpendicular will have a relative-velocity component and hence some 
doppler frequency shift; consequently the clutter spectrum from the altitude return will 
be of finite width. The shape of the altitude-return spectrum will depend upon the 




Altitude return 




fo-fr 



Frequency 



Transmitter to receiver leakage 
Main-lobe clutter 

-Target echo (head-on 

Receiver noise 

lAAAAAAAAAAAAAAAAAAAAAAAAAl 




fo+fr 



Fig. 4.48. Portion of the received signal spectrum in the vicinity of the RF carrier frequency /„, for a 
pulse-doppler AMTI radar. (After Maguire, 32 Proc. Natl. Conf. on Aeronaut. Electronics.) 

variation of the clutter cross section as a function of antenna depression angle (Sec. 
12.2). The cross section of the clutter directly beneath the aircraft for a depression 
angle of 90° can be quite large compared with that at small depression angles. The 
large cross section and the close range can result in considerable altitude return. 

The clutter illuminated by the antenna sidelobes in directions other than directly 
beneath the aircraft may have any relative velocity from +v to —v, depending on the 
angle made by the antenna beam and the aircraft vector velocity (v is the aircraft 
velocity). The clutter spectrum contributed by these sidelobes will extend 2vjX cps on 
either side of the transmitter frequency. The shape of the spectrum will depend upon 
the nature of the clutter illuminated and the shape of the antenna sidelobes. For 
purposes of illustration it is shown in Fig. 4.48 as a uniform spectrum. 



Sec. 4.9] 



MTI AND PULSE-DOPPLER RADAR 



161 



The ground clutter directly illuminated by the main beam of the antenna is also 
shown in Fig. 4.48. The doppler frequency shift of the main-beam clutter is 



2v , 
fc = — cos <j> 



(4.70) 



where cf> is the angle between the direction of the aircraft vector velocity and the axis of 
the antenna beam (Fig. 4.49). Also shown in this figure are the various sources of 
clutter signals. 

The finite antenna beamwidth results in a finite spread of the doppler frequency 
associated with the main-beam clutter. The spread is approximately 



A/ c = — sin <f> AcS = — - sin <f> 

A A 



(4.71) 



where A<f> was set equal to the antenna beamwidth 6 B . The negative sign produced on 
differentiation is ignored. The maximum doppler spread occurs when the beam is 



Radar 
aircraft 



-Simplified perimeter 
of elevation side-lobe 
pattern 

Direction of aircraft velocity 




Target aircraft 



Ground clutter 
Fig. 4.49. Sources of clutter signals. {After Maguire, zi Proc. Natl. Conf. on Aeronaut. Electronics.) 

perpendicular to the aircraft vector velocity. For example, if the radar antenna 
beamwidth were 2° and the wavelength 0. 1 m(f = 3,000 Mc) and if the aircraft velocity 
were 400 knots, the doppler- frequency spread would be 144 cps. (The maximum 
doppler frequency in this example corresponds to 4,120 cps.) Equation (4.71) indicates 
that the spread in doppler will be small if the beamwidth B and the depression angle cf> 
are small. 

The altitude return may be eliminated by turning the receiver off (gating) at that range 
corresponding to the altitude of the aircraft. Gating the altitude return has the dis- 
advantage that targets at ranges corresponding to the aircraft altitude will also be 
eliminated from the receiver. A better method of suppressing the altitude return in 
the pulse radar is to eliminate the signal in the frequency domain, rather than in the 
time domain, by inserting a rejection filter at the frequency f . The same rejection 
filter will also suppress the transmitter-to-receiver leakage. The clutter energy from 
the main lobe may also be suppressed by a rejection filter, but since the doppler frequency 
of this clutter component is not fixed, the rejection filter must be tunable and servo- 
controlled to track the main-lobe clutter as it changes because of scanning or because of 
changes in aircraft velocity. 

The position of the target echo in the frequency spectrum depends upon its velocity 
relative to that of the radar aircraft. If the target aircraft approaches the radar 
aircraft head on (from the forward sector), the doppler frequency shift of the target will 
be greater than the doppler shifts of the clutter echoes, as shown in Fig. 4.48. A filter 
can be used to exclude the clutter but pass the target echo. Similarly, if the targets are 
receding from one another along headings 180° apart, the target doppler frequency 



162 Introduction to Radar Systems [Sec. 4.9 

shift will again lie outside the clutter spectrum and may be readily separated from the 
clutter energy by filters. In other situations where the radar may be closing on the 
target from the tail or from the side, the relative velocities may be small and the target 
doppler will lie within the clutter doppler spectrum. In such situations the target echo 
must compete with the clutter energy for recognition. A large part of the clutter 
energy may be removed with a bank of fixed narrowband filters covering the expected 
range of doppler frequencies. The bandwidth of each individual filter must be wide 
enough to accept the energy contained in the target echo signal. The width of the filter 
will depend upon the time on target, equipment fluctuations, and other effects which 
broaden the echo-signal spectrum as discussed previously. Each filter may be followed 
by range gates and integrators. The use of a parallel bank of niters lowers the sensi- 
tivity of detection somewhat, because the increased false-alarm rate of a filter bank as 
compared with a single filter must be compensated by increasing the threshold of 
detection. However, the loss is small. The chief limitation of a fixed bank of doppler 
niters is the additional equipment complexity. If only a few targets are expected, 
narrowband doppler tracking filters might be used, one for each target. The filter 
must search through the expected doppler range before it can "lock on." If the radar 
receiver must search in both range and doppler to find its target, a relatively long search 
time might be required. 

In spite of its complexities and its shortcomings, a pulse-doppler radar is one of the 
better techniques for AMTI application. 

REFERENCES 

1. Ridenour, L. N.: "Radar System Engineering," MIT Radiation Laboratory Series, vol. 1, chap. 
16, McGraw-Hill Book Company, Inc., New York, 1947. 

2. Solomon, K. : A Double Delay and Subtraction Airborne Clutter Canceller, Proc. Conf. on 
Military Electronics (IRE), 1958, pp. 235-240. 

3. Eastwood, E., T. R. Blakemore, and B. J. Witt: Marconi Coherent MTI Radar on 50 Cms, 
Marconi Rev., vol. 19, 2d quarter, no. 121, pp. 53-60, 1956. 

4. Emslie, A. G.: Moving Target Indication on MEW, MIT Radiation Laboratory Rept. 1080, Feb. 
19,1946. J r 

5. Tanter, H.: Radar Receiver with Elimination of Fixed-target Echoes, Elect. Commun., vol 31 
pp. 235-248, December, 1954. 

6. Gager, C. : Transistorized MTI Canceller, Airborne Instruments Laboratory Monograph from 
Pulse of Long Island (IRE), February, 1960. 

7. Chance, ,B., R. I. Hulsizer, E. F. MacNichol, and F. C. Williams (eds.): "Electronic Time 
Measurements," MIT Radiation Laboratory Series, vol. 20, chap. 12, McGraw-Hill Book 
Company, Inc., New York, 1949. 

8. Blackburn, J. F. (ed.): "Components Handbook," MIT Radiation Laboratory Series, vol. 17, 
chap. 7, McGraw-Hill Book Company, Inc., New York, 1948. 

9. Chance, B., F. C. Williams, V. W. Hughes, D. Sayre, and E. F. MacNichol, Jr. (eds.) : "Waveforms," 
MIT Radiation Laboratory Series, vol. 19, chap. 23, McGraw-Hill Book Company, Inc., New 
York, 1949. r J> > 

10. Emslie, A. G.: Moving Target Indication on MEW, MIT Radiation Laboratory Rept. 1080, 
Feb. 19, 1946. J ^ 

11. Arenberg, D. L.: Ultrasonic Solid Delay Lines, J. Acous. Soc. Am., vol. 20, pp. 1-28, January, 

12. Huntington, H. B., A. G. Emslie, and V. W. Hughes: Ultrasonic Delay Lines, Pt. I, /. Franklin 
Inst., vol. 245, pp. 1-24, January, 1948; Emslie, A. G., H. B. Huntington, H. Shapiro, and A. E. 
Benfield, Pt. II, pp. 101-115, February, 1948. 

13. Arenberg, D. L.: Ultrasonic Delay Lines, IRE Natl. Conv. Record, 1954. 

14. Bliley Electric Co.: Bulletin 48, Erie, Pa., 1955. 

15. May, J. E., Jr. : Low-loss 1000 Microsecond Ultrasonic Delay Lines, Proc. Natl. Electronics Conf., 
vol. 11, pp. 786-790, 1955. 

16. Bendat, J. S.: "Principles and Applications of Random Noise Theory," pp. 114-118 John Wiley 
& Sons, Inc., New York, 1958. 

17. Perlman, S. E.: Staggered Rep Rate Fills Radar Blind Spots, Electronics, vol. 31, no 47 pp 
82-85, Nov. 21, 1958. VV ' 



MTI AND PULSE-DOPPLER RADAR 163 

18. White, W. D., and A. E. Ruvin: Recent Advances in the Synthesis of Comb Filters, IRE Natl. 
Conv. Record, vol. 5, pt. 2, pp. 186-199, 1957. 

19. White, W. D.: Synthesis of Comb Filters, Proc. Natl. Conf. on Aeronaut. Electronics, 1958, 
pp. 279-285. 

20. Urkowitz, H.: Analysis and Synthesis of Delay Line Periodic Filters, IRE Trans., vol. CT-4, 
pp. 41-53, June, 1957. 

21. McKee, D. A.: An FM MTI Cancellation System, MIT Lincoln Lab. Tech. Rept. 171, Jan. 8, 
1958. 

22. Ruvin, A.: Blower Vibration and MTI, Airborne Instruments Laboratory Monograph from 
Pulse of Long Island (IRE), April, 1959. 

23. Stephenson, J. G.: Designing Stable Tunable Microwave Oscillators, Electronics, vol. 28, pp. 
184-187, March, 1955. 

24. Dauksher, W. J.: Stable Local Oscillator for S-band Radar, Electronics, vol. 29, pp. 179-181, 
September, 1956. 

25. Goldstein, H.: The Effect of Clutter Fluctuations on MTI, MIT Radiation Lab. Rept. 700, Dec. 
27, 1945. 

26. Swerling, P. : Probability of Detection for Fluctuating Targets, IRE Trans., vol. IT-6, pp. 269-308, 
April, 1960. 

27. Barlow, E. J. : Doppler Radar, Proc. IRE, vol. 37, pp. 340-355, April, 1949. 

28. Grisetti, R. S., M. M. Santa, and G. M. Kirkpatrick: Effect of Internal Fluctuations and Scanning 
on Clutter Attenuation in MTI Radar, IRE Trans., vol. ANE-2, no. 1, pp. 37^1, March, 1955. 

29. Kroszczynski. J. : Efficiency of Attenuation of Constant Echoes in Simple and Double Cancella- 
tion Apparatus, Prace, Przem. Inst. Tele., vol. 8, no. 24, pp. 41-46, 1958. (Translated by 
Morris D. Friedman, MIT Lincoln Laboratory.) 

30. Anderson, D. B. : A Microwave Technique to Reduce Platform Motion and Scanning Noise in 
Airborne Moving-target Radar, IRE WESCON Conv. Record, vol. 2, pt. 1, pp. 202-211, 1958. 

31. Sargent, R. S.: Moving Target Detection by Pulse Doppler Radar, Electronics, vol. 27, no. 9, 
pp. 138-141, September, 1954. 

32. Maguire, W. W.: Application of Pulsed Doppler Radar to Airborne Radar Systems, Proc. 
Natl. Conf. on Aeronaut. Electronics (Dayton, Ohio), pp. 291-295, 1958. 

33. Richardson, R. E.: Some Pulse-doppler Radar Design Considerations, MIT Lincoln Lab. Tech. 
Rept. 154, Aug. 12, 1957. 

34. George, T. S. : Fluctuations of Ground Clutter Return in Airborne Radar Equipment, Proc. IEE, 
vol. 99, pt. IV, no. 2, pp. 92-99, April, 1952. 

35. Dickey, F. R., Jr.: Theoretical Performance of Airborne Moving Target Indicators, IRE Trans., 
PGAE-8, pp. 12-23, June, 1953. 

36. Urkowitz, H.: An Extension to the Theory of the Performance of Airborne Moving-target 
Indicators, IRE Trans., vol. ANE-5, pp. 210-214, December, 1958. 

37. Bauer, P.A. : Low Temperature Coefficient Ultrasonic Solid Delay Lines, Solid State J., vol. 2, 
no. 12, pp. 23-29, December, 1961. 



5 



TRACKING RADAR 



5.1. Tracking with Radar 

A tracking-radar system measures the coordinates of a target and provides data which 
may be used to determine the target path and to predict its future position. All or only 
part of the available radar data — range, elevation angle, azimuth angle, and doppler 
frequency shift— may be used in predicting future position; that is, a radar might track 
in range, in angle, in doppler, or with any combination. Almost any radar can be 
considered a tracking radar provided its output information is processed properly. 
But, in general, it is the method by which angle tracking is accomplished that distin- 
guishes what is normally considered a tracking radar from any other radar. It is also 
necessary to distinguish between a continuous tracking radar and a track-while-scan 
(TWS) radar. The former supplies continuous tracking data on a particular target, 
while the track-while-scan supplies sampled data on many targets. In general, the 
continuous tracking radar and the TWS radar employ different types of equipment. 

The antenna beam in the continuous tracking radar is positioned in angle by a 
servomechanism actuated by an error signal. The various methods for generating the 
error signal may be classified as sequential lobing, conical scan, and simultaneous lobing 
or monopuhe. The range and doppler frequency shift can also be continuously 
tracked, if desired, by a servo-control loop actuated by an error signal generated in the 
radar receiver. The information available from a tracking radar may be presented on a 
cathode-ray-tube (CRT) display for action by an operator, or it may be supplied to an 
automatic computer which determines the target path and calculates its probable 
future course. 

The tracking radar must first find its target before it can track. Some radars, such as 
the SCR-584, operate in a search mode in order to find the target before switching to a 
tracking mode. Although it is possible to use a single radar for both the search and the 
tracking functions, such a procedure usually results in certain operational limitations. 
Obviously, when the radar is used in its tracking mode, it has no knowledge of other 
potential targets. Also, if the antenna pattern is a narrow pencil beam and if the search 
volume is large, a relatively long time might be required to find the target. Therefore 
many radar tracking systems employ a separate search radar to provide the information 
necessary to position the tracker on the target. A search radar, when used for this 
purpose, is called an acquisition radar. 

In some applications, separate search and track radars may not be practical or even 
desirable. An example is the airborne interception (AI) radar, in which the angular 
search volume is not too large and is usually restricted to the forward sector only. In 
addition, there is usually little room to spare in an aircraft for two separate radars. 
Even in those applications where a separate radar supplies acquisition information, the 
tracker usually will have to perform some limited angular search in order to find the 
target. 

The scanning fan-beam search radar can also provide tracking information to 
determine the path of the target and predict its future position. Each time the radar 
beam scans past the target, its coordinates are obtained. If the change in target 
coordinates from scan to scan is not too large, it is possible to reconstruct the track of 

164 



Sec. 5.2] Tracking Radar 165 

the target. This is called track-while-scan. It provides tracking information on a 
discrete, or sampled, basis rather than continuously. The simplest manifestation of a 
TWS radar may be had by providing the PPI-scope operator with a grease pencil to 
mark the target pips on the face of the scope. A line joining those pips that correspond 
to the same target provides the target track. When the traffic is so dense that human 
operators cannot maintain pace with the information available from the radar, the 
target trajectory data may be processed automatically in a digital computer as is done 
in the SAGE air defense system. Whenever the term tracking radar is used in this book, 
it refers to the continuous tracker rather than to track-while-scan, unless otherwise 
specified. 

The chief use of the continuous tracking radar has been for the control of military 
weapons such as antiaircraft artillery and missile guidance. Tracking radars are used 
also for guidance in the launchings of satellites and space vehicles. Because of their 
versatility, tracking radars often have been used for general-purpose instrumentation 
or as a research tool. 

5.2. Sequential Lobing 

The antenna pattern commonly employed with tracking radars is the symmetrical 
pencil beam in which the elevation and azimuth beamwidths are essentially equal. A 
pencil-beam antenna has many advantages for tracking-radar applications. It 
provides high gain by concentrating the radiated power in the direction of the target. 
It reduces unwanted echoes from other targets and from the ground. The angular 
coordinates of the target can be determined more precisely than with a fan beam. 
However, a simple pencil-beam antenna is not suitable for tracking radars unless means 
are provided for determining the magnitude and direction of the target's angular 
position with respect to some reference direction, usually the axis of the antenna. The. 
difference between the target position and the reference direction is the angular error. 
The tracking radar attempts to position the antenna to make the angular error zero. 
When the angular error is zero, the target is located along the reference direction. 

One method of obtaining the direction and the magnitude of the angular error in one 
coordinate is by alternately switching the antenna beam between two positions (Fig. 
5.1). This is called lobe switching, sequential switching, or sequential lobing. Figure 
5.1a is a polar representation of the antenna beam (minus the sidelobes) in the two 
switched positions. A plot in rectangular coordinates is shown in Fig. 5.1Z>, and the 
error signal obtained from a target not on the switching axis (reference direction) is 
shown in Fig. 5.1c. The difference in amplitude between the voltages obtained in the 
two switched positions is a measure of the angular displacement of the target from the 
switching axis. The sign of the difference determines the direction the antenna must be 
moved in order to align the switching axis with the direction of the target. When the 
voltages in the two switched positions are equal, the target is on axis and its position 
may be determined from the axis direction. 

Two additional switching positions are needed to obtain the angular error in the 
orthogonal coordinate. Thus a two-dimensional sequentially lobing radar might 
consist of a cluster of four feed horns illuminating a single antenna, arranged so that the 
right-left, up-down sectors are covered by successive antenna positions. Both trans- 
mission and reception are accomplished at each position. A cluster of five feeds might 
also be employed, with the central feed used for transmission while the outer four feeds 
are used for receiving. High-power RF switches are not needed since only the receiving 
beams, and not the transmitting beam, are stepped in the five-feed arrangement. 

One of the limitations of a simple unswitched nonscanning pencil-beam antenna is 
that the angle accuracy can be no better than the size of the antenna beamwidth. An 
important feature of sequential lobing (as well as the other tracking techniques to be 



166 



Introduction to Radar Systems 



[Sec. 5.3 



discussed) is that the target-position accuracy can be far better than that given by the 
antenna beamwidth. The accuracy depends on how well equality of the signals in the 
switched positions can be determined. The fundamental limitation to accuracy is 
system noise caused either by mechanical or electrical fluctuations. 

Sequential lobing, or lobe switching, was one of the first tracking-radar techniques to 
be employed. Early applications were in airborne-interception radar, where it 
provided directional information for homing on a target, and in ground-based anti- 
aircraft fire-control radars such as the SCR-268. It is not used as often in modern 
tracking-radar applications as some of the other techniques to be described. 





Time 



Fig. 5.1. Lobe-switching antenna patterns and error signal (one dimension), (a) Polar representation 
of switched antenna patterns; (ft) rectangular representation; (c) error signal. 

5.3. Conical Scan 

A logical extension of the simultaneous lobing technique described in the previous 
section is to rotate continuously an offset antenna beam rather than discontinuously 
step the beam between four discrete positions. This is known as conical scanning 
(Fig. 5.2). The angle between the axis of rotation (which is usually, but not always, the 
axis of the antenna reflector) and the axis of the antenna beam is called the squint angle. | 
Consider a target at position A. The echo signal will be modulated at a frequency equal 
to the rotation frequency of the beam. The amplitude of the echo-signal modulation 
will depend upon the shape of the antenna pattern, the squint angle, and the angle 
between the target line of sight and the rotation axis. The phase of the modulation 
depends on the direction of the angle between the target and the rotation axis. The 
conical-scan modulation isextracted fromtheecho signal and applied to a servo-control 
system which continuallypositionstheantennaon the target. [Note that two servos are 



t The squint angle is also sometimes used to describe the angle between the two major lobe axes in a 
lobe-switching antenna (IRE Standards 54 IRE 12 S 1), but this use of the term is not employed here. 



Sec. 5.3] 



Tracking Radar 167 



required because the tracking problem is two-dimensional. Both the rectangular 
(az-el) and polar tracking coordinates may be used . ] When the antenna is on target, as 
in B of Fig. 5.2, the line of sight to the target and the rotation axis coincide, and the 
conical-scan modulation is zero. 

A block diagram of the angle-tracking portion of a typical conical-scan tracking radar 
is shown in Fig. 5.3. The antenna is mounted so that it can be positioned in both 



Target axis - 




Beam 
rotation 



Radar 



Fig. 5.2. Conical-scan tracking. 



azimuth and elevation by separate motors, which might be either electric- or hydraulic- 
driven. The antenna beam is offset by tilting either the feed or the reflector with 
respect to one another. 

One of the simplest conical-scan antennas is a parabola with an offset rear feed 
rotated about the axis of the reflector. If the feed maintains the plane of polarization 
fixed as it rotates, it is called a nutating feed. A rotating feed such as is used in the 









Transmitter 
































Receiver 
with 
AGC 












To rotary joint 




Duplexer 






Third 
detector 




Error-signal 
filter 




on antenna /— 




























Ref. 
aen.x 


smZw^t 
















^/1-j//" 


31 


cos 


Zirf s t 




■ 




' 


Error \ 


n%p& 




Elevation 

servo 
amplifier 






Elevation-angle 
error detector 




signal 


U%s,& 


Elevat 


on 










Scan ,^< /£•» 
motor — ^ T 


motor 










\ 


















Azimuth 

servo 
amplifier 




Azimuth-ongle 
error detector 






servo motor -r 

































Fig. 5.3. Block diagram of conical-scan tracking radar. 

SCR-584 rotates a dipole and thus rotates polarization. The latter type of feed 
requires a rotary joint. The nutating feed requires a flexible joint. If the antenna is 
small, it may be easier to rotate the dish, which is offset, rather than the feed, thus 
avoiding the problem of a rotary or flexible RF joint in the feed. A typical conical-scan 
rotation speed might be 30 rps (1 ,800 rpm) . The same motor that provides the conical- 
scan rotation of the antenna beam also drives a two-phase reference generator with two 



168 Introduction to Radar Systems [Sec. 5.3 

outputs 90° apart in phase. These two outputs serve as a reference to extract the eleva- 
tion and azimuth errors. The received echo signal is fed to the receiver from the antenna 
via two rotary joints (not shown in the block diagram). One rotary joint permits 
motion in azimuth; the other, in elevation. 

The receiver is a conventional superheterodyne except for two features peculiar to 
the conical-scan tracking radar. One feature not found in other radar receivers is a 
means of extracting the conical-scan modulation, or error signal. This is accomplished 
after the second detector in the video portion of the receiver. In the block diagram 
this function is indicated as the third detector. The purpose of the low-pass error- 
signal filter is to remove the harmonics of the conical-scan frequency, the prf, and the 
harmonics of the prf if they are present. The error signal is compared with the elevation 
and azimuth reference signals in the angle-error detectors, which are phase-sensitive 
detectors. 1-5 A phase-sensitive detector is a nonlinear device in which the input signal 
(in this case the angle-error signal) is mixed with the reference signal. The input and 
reference signals are of the same frequency. The output d-c voltage reverses polarity 
as the phase of the input signal changes through 180°. The magnitude of the d-c 
output from the angle-error detector is proportional to the error, and the sign (polarity) 
is an indication of the direction of the error. The angle-error-detector outputs are 
amplified and drive the antenna elevation and azimuth servo motors. When the 
antenna is directly on target, the error signal is zero. 

The angular position of the target may be determined from the elevation and azimuth 
of the antenna axis. The position can be read out by means of standard angle trans- 
ducers such as synchros, potentiometers, or analog-to-digital-data converters. 

The difference between the phase-sensitive detector and phase detector is often one of 
actual operating conditions. 5 The phase detector measures the phase difference 
between two sinusoidal signals of the same frequency. In the phase-sensitive detector 
the output voltage reverses polarity as the phase of the input changes through 180°. 
Identical circuits can be used for phase measurement and for phase-sensitive detection. 
It is usually assumed that the amplitudes of the reference and the input signal are the 
same in the phase detector, while in the phase-sensitive detector, the reference is much 
larger than the input signal. 

Boxcar Generator. The purpose of the third detector and filter is to pass the modula- 
tion at the conical-scan frequency and to reject the pulse repetition frequency and its 
harmonics. In the early S-band version of the SCR-584, this was accomplished with a 
more or less conventional amplitude detector and filter. In the Z-band version and in 
most modern radars the filtering function is performed with a device called the boxcar 
generator. 6 The boxcar generator was also mentioned in the discussion of the MTI 
receiver using range-gated filters (Sec. 4.4). In essence, it clamps or stretches the video 
pulses of Fig. 5.4a in time so as to cover the entire pulse-repetition period (Fig. 5Ab). 
This is possible only in a range-gated receiver. (Tracking radars are normally operated 
with range gates.) The boxcar generator consists of an electric circuit that clamps the 
potential of a storage element, such as a capacitor, to the video-pulse amplitude each 
time the pulse is received. The capacitor maintains the potential of the pulse during the 
entire repetition period and is altered only when a new video pulse appears whose 
amplitude differs from the previous one. The boxcar generator eliminates the pulse 
repetition frequency and reduces its harmonics. It also has the practical advantage 
that the magnitude of the conical-scan modulation is amplified because pulse stretching 
puts more of the available energy at the modulation frequency. The pulse repetition 
frequency must be sufficiently large compared with the conical-scan frequency for 
proper boxcar filtering. If not, it may be necessary to provide additional filtering to 
attenuate undesired cross-modulation frequency components. 

Automatic Gain Control. 1 - 9 The echo-signal amplitude at the tracking-radar 



Sec. 5.3] 



Tracking Radar 



169 



receiver will not be constant but will vary with time. The three major causes of 
variation in amplitude are (1) the inverse-fourth-power relationship between the echo 
signal and range, (2) the conical-scan modulation (angle-error signal), and (3) ampli- 
tude fluctuations in the target cross section. The function of the automatic gain 
control (AGC) is to maintain the d-c level of the receiver output constant and to 
smooth or eliminate as much of the noiselike amplitude fluctuations as possible without 
disturbing the extraction of the desired error signal at the conical-scan frequency. 





N. ^.j* 


s 


V 


K 


*^-- 






-») 


-Vtr 




(a) 











































-Vtr 




(A) 









Fig. 5.4. (a) Pulse train with conical-scan modulation; (Z>) same pulse train after passing through 
boxcar generator. 

One of the purposes of AGC in any receiver is to prevent saturation by large signals. 
The scanning modulation and the error signal would be lost if the receiver were to 
saturate. In the conical-scan tracking radar an AGC that maintains the d-c level 
constant results in an error signal that is a true indication of the angular pointing error. 
It is shown later in this section (during the derivation of the error-signal voltage) that the 
d-c level of the receiver must be maintained constant if the angular error is to be linearly 
related to the angle-error signal voltage. 



















Range 
gate and 
boxcar 


Conical scan modulation 


mixer 


IF 
amplifier 


> ■ 


2d 
det. 




Video 
amplifier 


to angle-error detector 












. 
















. 




' 


' 






0-c 
amplifier 


AGC 
filter 

























T 

Delay voltage V c 
Fig. 5.5. Block diagram of the AGC portion of a tracking-radar receiver. 



An example of the AGC portion of a tracking-radar receiver is shown in Fig. 5.5. 
A portion of the video-amplifier output is passed through a low-pass or smoothing 
filter and fed back to control the gain of the IF amplifier. The larger the video output, 
the larger will be the feedback signal and the greater will be the gain reduction. The 
filter in the AGC loop should pass all frequencies from direct current to just below the 



170 Introduction to Radar Systems [Sue. 5.3 

conical-scan-modulation frequency. The loop gain of the AGC filter measured at the 
conical-scan frequency should be low so that the error signal will not be affected by AGC 
action. If the AGC responds to the conical-scan frequency, the error signal might 
be lost. The phase shift of this filter must be small if its phase characteristic is not to 
influence the error signal. A phase change of the error signal is equivalent to a rotation 
of the reference axes and introduces cross coupling, or "cross talk," between the 
elevation and azimuth angle-tracking loops. Cross talk affects the stability of the 
tracking and might result in an unwanted nutating motion of the antenna. In con- 
ventional tracking-radar applications the phase change introduced by the feedback-loop 
filter should be less than 10°, and in some applications it should be as little as 2°. 8 For 
this reason, a filter with a sharp attenuation characteristic in the vicinity of the conical- 
scan frequency might not be desirable because of the relatively large amount of phase 
shift which it would introduce. 

The output of the feedback loop will be zero unless the feedback voltage exceeds a 
prespecified minimum value V c . In the block diagram the feedback voltage and the 
voltage V c are compared in the d-c amplifier. If the feedback voltage exceeds V c , the 
AGC is operative, while if it is less, there is no AGC action. The voltage V c is called the 
delay voltage. The terminology may be a bit misleading since the delay is not in time 
but in amplitude. The purpose of the delay voltage is to provide a reference for the 
constant output signal and permit receiver gain for weak signals. If the delay voltage 
were zero, any output which might appear from the receiver would be due to the failure 
of the AGC circuit to regulate completely. 

In many applications of AGC the delay voltage is actually zero. This is called 
undelayed AGC. In such cases the AGC can still perform satisfactorily since the loop 
gain is usually low for small signals. Thus the AGC will not regulate weak signals. 
The effect is similar to having a delay voltage, but the performance will not be as good. 

The required dynamic range of the AGC will depend upon the variation in range over 
which targets are tracked and the variations expected in the target cross section. If 
the range variation were 10 to 1 , the contribution to the dynamic range would be 40 db. 
The target cross section might also contribute another 40-db variation. Another 
10 db ought to be allowed to account for variations in the other parameters of the radar 
equation. Hence the dynamic range of operation required of the receiver AGC might 
be of the order of 90 db, or perhaps more. 

It is found 8 in practice that the maximum gain variation which can be obtained with a 
single IF stage is of the order of 40 db. Therefore two to three stages of the IF amplifier 
must be gain-controlled to accommodate the total dynamic range. The middle stages 
are usually the ones controlled since the first stage gain should remain high so as not to 
influence the noise figure of the mixer stage. It is also best not to control the last IF 
stage since the maximum undistorted output of an amplifying stage is reduced when its 
gain is reduced by the application of a control voltage. 

An alternative AGC filter design would maintain the AGC loop gain up to frequencies 
much higher than the conical-scan frequency. The scan modulation would be effec- 
tively suppressed in the output of the receiver, and the output would be used to measure 
range in the normal manner. In this case, the error signal can be recovered from the 
AGC voltage since it varies at the conical-scan frequency. The AGC voltage will also 
contain any amplitude fluctuations that appear with the echo signal. The error signal 
may be recovered from the AGC voltage with a narrow bandpass filter centered at the 
scan-modulation frequency. 

Error Signal. The error signal from the conical-scan tracker will be derived assuming 
that a properly designed AGC eliminates all signal modulations except the conical-scan 
modulation. 
Consider an echo pulse train with conical-scan modulation as shown in Fig. 5.4a. 



Sec, 5.3] Tracking Radar 171 

The pulse repetition frequency is f r , and the pulse width is t. Assuming a linear 
detector, the video pulse train may be represented by the expression 10 

V{t) = K'G{t)F k {t) (5.1) 

where K' = constant determined by design of AGC (without AGC, K' is determined 
by parameters of radar equation) 
G(i) = modulation due to antenna pattern 
F k (t) = waveform representing unmodulated pulse train 
= llfor k/f r < t < k/f r + r 
\0 otherwise 
k = integer = 0, 1, 2, . . . 
Equation (5.1) will be expanded to obtain the various frequency components contained 
in the received signal. First the expression for the antenna modulation factor G(t) will 
be derived. The two-way-voltage (or one-way-power) antenna pattern may be 
approximated by the Gaussian function 

G(6) = G exp {-aW) (5.2) 

where 6 — angle between antenna-beam axis and target axis 

G = maximum antenna gain, that is, value of G(0) at 8 = 
a 2 = constant = 2.716/6%, where 6 is measured in degrees and 6 B , also in 
degrees, is antenna beamwidth measured between 3-db, or half-power, 
points, of antenna pattern 
Referring to Fig. 5.6a, the angle Q q is the squint angle denned by the antenna-beam 
axis and the axis of rotation; 9 T is the angle between the axis of rotation and the target 
axis ; <f> is the rotation angle of the conical scanner as measured from some arbitrary 
phase reference ; and cj> is the angle defined by the target and the reference axis. The 
angles 6, 6 Q , 6 T may also be defined by the lengths of arc Rd, R6 g , Rd T on a sphere of 
radius R (Fig. 5.6b). Since the distances Rd, R6 q , R6 T are small, they may be related by 
the law of cosines to the angle <f> — cf> . 

{R6f = (Rd Q f + (R6 T f + 2R*6 g e T cos (<f> - <£ ) (5.3) 

Substituting 6 2 as given by Eq. (5.3), into Eq. (5.2), with G = 1, gives 

G(0) = exp \_-a\d\ + 2 T )] exp [-2a%6 T cos (<f> - O }] (5.4) 

The following relationship may be derived from expressions for Bessel functions given 
by Whittaker and Watson 11 

00 

exp (—x cos f) = I (x) + 2 ^ l n ( x ) cos "V (5-5) 

n = l 

where /„ is the nth-order Bessel function of imaginary coefficient. 
Using the above relationship, Eq. (5.4) may be written as 



G(0 = exp i-a\d\ + 6%)-] 



I (2a\d T ) + 2 2 I n (2a%6 T ) cos (2rrnf s t - n<j> ) 



i = \ 



(5.6) 



In Eq. (5.6) 2irf s t has been substituted for </>, where/, is the conical-scan frequency. To 
simplify the algebra, let 

K" = {exp 1-aXdl + d\)-}}I (2a\0 T ) K n = ^ff^ 

I {2a l 6 q e T ) 



172 Introduction to Radar Systems [Sec. 5.3 

Substituting the above in Eq. (5.6), the antenna scan-modulation factor becomes 



G(0 = K" 



1 + 2 K n C° s (27771/;* — n<f> ) 
n = l 



(5.7) 




Target 




Locus of 
antenna-beam center 



Fig. 5.6. (a) Geometry and symbols for derivation of conical-scan error signal; (b) head-on view of 
conical-scan antenna beam. 



The factor F k {t) in Eq. (5.1) is the rectangular pulse train of unit amplitude. The 
Fourier series expansion of F k (i) is 



F k (t)=f r r 



1 + 2, K m cos 2nmf r 



H)] 



(5.8) 



where 



K = 2 sin mTTTyr 
rmrf r T 



Sec. 5.3] Tracking Radar 173 

Substituting Eqs. (5.7) and (5.8) into Eq. (5.1) gives the video voltage. 



no 



:'K"f r r(l + | K n cos (2rrnf s t - n<f> ) 

\ n = l 

+ J t K m cos2^mf r (t-l) 

m = X \ 2/ 



OD 00 If If 

2 2 ^P {cos |>(m/ r + n/.)f - nmf r T - n^ ] 



+ cos \2v{mf r - n/,)f - 77/n/ r T + «&,]}) (5-9) 



The theoretical conical-scan-modulated echo signal as represented by Eq. (5.9) 
consists of four parts : 

1 . A d-c component of magnitude K'K"f r T 

2. An infinite number of a-c components corresponding to the conical-scan frequency 
f s and its harmonics nf s 

3. An infinite number of a-c components corresponding to the pulse repetition 
frequency f r and its harmonics mf r 

4. An infinite number of sidebands ±nf s centered about the prf,/ r , and its harmonics 
Each of these components has a different amplitude, and in a practical radar, the 

number of harmonics would be finite. The only component of interest is the modula- 
tion at the conical-scan frequency /,. If it can be assumed that/ r >/, and that a 
suitable low-pass filter permits only the direct current and the scan frequency f s to pass, 
the error signal becomes 

1/(0 = K'K"f T r + 2K'f r r exp [-a 2 (0 2 + fl a r )]/i(2a 2 c M cos (2vf t t - fa) (5.10) 

The error signal represented by Eq. (5.10) is fed into both the azimuth and the elevation 
angle-error detectors. In the angle-error detectors, which are phase-sensitive detectors, 
the horizontal and vertical projections of the target angle T are extracted. One of the 
angle-error detectors (for example, the azimuth channel) is supplied with a reference 
signal V r cos 2-nfj, while the other is supplied with V r sin 2nf s t. Both signals are 
derived from the reference generator mounted on the antenna scanner. (V r is the 
magnitude of the reference-signal voltage.) 

The output of the azimuth-error detector is a d-c voltage proportional to the magni- 
tude of the a-c component of the error signal of Eq. (5.10) times the magnitude of the 
reference voltagej times the cosine of the phase difference between the two, <f> , or 

Azimuth-error signal = 2K'f r rV r exp [-a 2 (0* + 2 r )]/ 1 (2fl 2 e 9 r ) cos <j> (5.11) 

A plot of Eq. (5.1 1) as a function of d T /6 B and for various values of 6J6 B is shown in 
Fig. 5.7. For small angular error, Eq. (5.1 1) approaches the following; 

Azimuth-error signal <** C$ T cos <f> (5.12) 

where C 1 is a constant. Thus the output of the azimuth angular detector is a voltage 
directly proportional to the angular error if the error is small and if A" is maintained 
constant by the AGC. 

Likewise, the elevation-angle-error voltage for small error is proportional to 

Elevation-error signal m Cjd T sin <f> (5.13) 

The elevation- and azimuth-error signals are applied to their respective servo motors 
which position the antenna for zero-error signal. 

t In many cases, the phase-sensitive detector is designed so that the output amplitude is a function 
of the input signal only and is independent of the reference-signal amplitude. 5 This does not affect 
the above analysis. 



174 Introduction to Radar Systems [Sec. 5.3 

It should be noted that one of the properties of the phase-sensitive detector is that no 
cross talk exists between the two error channels even though the same error signal 
[Eq. (5.10)] is fed to both angle-error detectors. 

In the above analysis the error signal was extracted by passing the video voltage 
through a detector followed by a low-pass filter. This combination removes the d-c 
component and passes only the fundamental of the conical-scan frequency. Although 
this procedure was used in some early tracking radars and is illustrated in Fig. 5 . 3, it is 
usually more common to employ a boxcar generator in the video to accomplish essen- 
tially the same function, but with more gain. The error-signal voltage from the boxcar 



0.22 


1 1 1 


1 


1 i 1 


1 


0.20 


_. 








o> 


0, 








8 0.18 


°B / 










/a 6 






>'• 










'■§ 0. 1 6 








_ 


QJ 




/a 8 














~ 0.14 








_ 


O) 
















*Q2 




i 0.12 


II // 






_ 


■> 










|o.io 








- 


S 0.08 










L. 










UJ 

0.06 




Bb 


Antenna 
crossover, db 


- 


0.04 




0.2 
0.4 
0.6 


0.5 

1.95 

4.36 


- 


0.02 




0.8 


7.7 


- 





r 1 1 1 


I I 


I I i 





0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 

e T /e B 

Fig. 5.7. Plot of the relative error-signal from the conical-scan radar [Eq. (5.11)] as a function of 
target angle (6 T /6 B ) and squint angle (6JB B ). The angle <j>„ is assumed fixed. 

generator will be slightly different from that given by Eq. (5.10). To derive the error 
signal with the boxcar generator we start with the Fourier-series development of a train 
of flat-top pulses whose amplitude is proportional to the scan modulation. Note that 
this differs from the waveform represented by Eq. (5.9) in which the pulses were assumed 
to be amplitude-modulated by the conical-scan modulation rather than flat-topped. 
The Fourier series for a flat-top pulse train with a pulse repetition frequency/., modu- 
lated by the antenna conical-scan modulation of a Gaussian antenna pattern [Eq. 
(5.6)], is 6 - 12 



V{t) 



= K'K"(t 



fr 



\ T fr + 1 K n -^t sin nnf s T cos (2nnf s t - -nnf s r 

\ n = \ Ttn) s 

. 1 ^ 2 sin TrmrL 
+ - z cos • 

7T m = l m 



n^o) 



S 

.2-nmf r \t -^ 



1 00 QO 



K„f r 



sin Tn(mf r + nf s ) cos [27r(mf r + nf s )t - ttxxj s t - noS ] 



7Tm = ln = l \mf r + nf s 

f Jr . sin Mm/, - nf s ) cos \2ir{mf r - nf.)t - irnf s r + w ^ ]l) (5.14) 
mf r - nf, )/ 



Sec. 5.4] Tracking Radar 175 

The output of the boxcar generator is found by setting the pulse width t = \\f r in Eq 
(5.14). All terms containing the pulse repetition frequency and its harmonics nf r 
disappear. There remains a d-c component, a component at the conical-scan frequency 
f s , components at the harmonics of/ s , and components at frequencies mf r ± nf s . The 
latter components are negligible if f r >/,. In any event, a filter may be used to 
eliminate all but the scan frequency. The error signal is 

V e (t) = 2K' exp {-a\d\ + d^I^a^O T ) 4 sin ^ cos (lirfjt - ^ - A (5.15) 

■"}, fr ^ St ' 

The output of the azimuth angle-error detector is 
Azimuth-error signal 

= 2V r K' exp {-a\6l + 8 r )]'i(2a 2 W ^ sin ^ cos fe + <£ ) (5.16) 

Again, if the angle error T is small and/ r >/„ Eq. (5.16) becomes 

Azimuth-error signal «a C 2 T cos <j> (5.17) 

A similar expression may be found for the elevation error. There are two effects to 
be noted with the boxcar generator as compared with the conventional detector [Eq. 
(5.12)]. The voltage output of the boxcar generator is greater than that of the con- 
ventional detector for the same angular error by the ratio C 2 /Q = fjf s . Thus the 
boxcar generator is capable of greater gain. Also, it is necessary that/. >/ s for proper 
operation of the boxcar generator. If this relationship does not hold, unwanted 
modulation products will appear in the error signal, and the phase shift irfjf r in the last 
term of Eq. (5.16) can cause an erroneous indication if not compensated. 

5.4. Simultaneous Lobing or Monopulse 13-17 

In both the sequential-lobing and conical-scan tracking techniques, the measurement 
of angular error in two orthogonal coordinates (azimuth and elevation) requires that a 
minimum of three pulses be processed. In practice, however, the minimum number of 
pulses in sequential lobing is usually four — one per antenna position. Conical 
scanning usually requires more than four pulses to derive the error signal. In the time 
interval during which a measurement is made with either sequential lobing or conical 
scan, the echo pulses must contain no amplitude-modulation components other than 
the modulation produced by scanning. If the echo pulse train did contain additional 
modulation components, caused, for example, by a fluctuating target cross section, the 
tracking accuracy might be degraded, especially if the frequency components of the 
fluctuations were at or near the conical-scan frequency or the sequential-lobing rate. 
The effect of the fluctuating echo can be sufficiently serious in some applications to 
severely limit the accuracy of those tracking radars which require many pulses to be 
processed in extracting the error signal. 

Pulse-to-pulse amplitude fluctuations of the echo signal have no effect on tracking 
accuracy if the angular measurement is made on the basis of one pulse rather than many. 
There are several methods by which angle-error information might be obtained with 
only a single pulse. More than one antenna beam is used simultaneously in these 
methods, in contrast to the conical-scan or lobe-switching tracker, which utilizes one 
antenna beam on a time-shared basis. The angle of arrival of the echo signal may be 
determined in a single-pulse system by measuring the relative phase or the relative 
amplitude of the echo pulse received in each beam. The names simultaneous lobing and 
monopulse are used to describe those tracking techniques which derive angle-error 
information on the basis of a single pulse. 



176 



Introduction to Radar Systems 



[Sec. 5.4 



An example of a simultaneous-lobing technique is amplitude-comparison monopulse, 
or more simply, monopulse. In this technique the RF signals received from two 
offset antenna beams are combined so that both the sum and the difference signals are 
obtained simultaneously. The sum and difference signals are multiplied in a phase- 
sensitive detector to obtain both the magnitude and the direction of the error signal. 
All the information necessary to determine the angular error is obtained on the basis of a 
single pulse; hence the name monopulse is quite appropriate. 

Amplitude-comparison Monopulse. 13 The amplitude-comparison monopulse em- 
ploys two overlapping antenna patterns (Fig. 5.Sa) to obtain the angular error in one 
coordinate. The two overlapping antenna beams may be generated with a single 
reflector or with a lens antenna illuminated by two adjacent feeds. (A cluster of four 







(a) 



(c) 




Angle 



(/>) 



(d) 



Fig. 5.8. Monopulse antenna patterns and error signal. Left-hand diagrams in (a-c) are in polar 
coordinates; right-hand diagrams are in rectangular coordinates, (a) Overlapping antenna patterns; 
(b) sum pattern; (c) difference pattern; (d) product (error) signal. 



feeds may be used if both elevation- and azimuth-error signals are wanted.) The sum 
of the two antenna patterns of Fig. 5.8a is shown in Fig. 5.8Z>, and the difference in Fig. 
5.8c. The sum pattern is used for transmission, while both the sum pattern and the 
difference pattern are used on reception. The signal received with the difference 
pattern provides the magnitude of the angle error. The sum signal provides the range 
measurement and is also used as a reference to extract the sign of the error signal. 
Signals received from the sum and the difference patterns are amplified separately and 
combined in a phase-sensitive detector to produce the error-signal characteristic shown 
in Fig. 5.8d. 

A block diagram of the amplitude-comparison-monopulse tracking radar for a single 
angular coordinate is shown in Fig. 5.9. The two adjacent antenna feeds are connected 
to the two arms of a hybrid junction such as a "magic T," a "rat race," or a short-slot 
coupler. 18 The sum and difference signals appear at the two other arms of the hybrid. 
On reception, the outputs of the sum arm and the difference arm are each heterodyned 
to an intermediate frequency and amplified as in any superheterodyne receiver. The 



Sec. 5.4] 



Tracking Radar 177 



transmitter is connected to the sum arm. Range information is also extracted from the 
sum channel. A duplexer is included in the sum arm for the protection of the receiver. 
The output of the phase-sensitive detector is an error signal whose magnitude is pro- 
portional to the angular error and whose sign is proportional to the direction. 

In Fig. 5.9 the output of the phase-sensitive detector (angle information) and the sum 
channel (range information) are shown presented on the A-scope. The sum-channel 
signal operates the A-scope just as in a normal radar. It gives an indication of the 
target range by deflecting the beam upward, generating a pip. The output of the phase- 
sensitive detector, however, modifies the scope sweep to deflect the target pip either to 
the right or to the left, depending upon the sign of the angular error. The amount of 
leaning is a measure of the magnitude of the angular error. This presentation has been 
called the "Pisa" indicator, after the famous leaning tower. 13 



Tronsmitter 



Sum chonnel 



TR 




^Hybrid 
junction 



IF 
omplifier 



LO 



Antenno 
feeds 



Amplitude 
detector 



Range 
signal 



Phose- 
sensitive 
detector 



Mixer 



IF 
amplifier 



Angle- 
error 
signal 



A-scope 



Sum 
circuit 



Difference chonnel 




Sweep 
generator 



Fig. 5.9. Block diagram of amplitude-comparison-monopulse radar (one angular coordinate). 

The output of the monopulse radar may also be used to perform automatic tracking. 
The angular-error signal may actuate a servo-control system to position the antenna, 
and the range output from the sum channel may be fed into an automatic-range- 
tracking unit. 

The sign of the difference signal (and the direction of the angular error) is determined 
by comparing the phase of the difference signal with the phase of the sum signal. If the 
sum signal in the IF portion of the receiver were A s cos a> IF t, the difference signal would 
be either A d cos a> 1F t or — A d cos a> lF t (A s > 0, A d > 0), depending on which side of 
center is the target. Since — A d cos co IF t = A d cos co IF (t + tt), the sign of the differ- 
ence signal may be measured by determining whether the difference signal is in phase 
with the sum signal or 180° out of phase. 

Although a phase comparison is a part of the amplitude-comparison-monopulse 
radar, the angular-error signal is basically derived by comparing the echo amplitudes 
from simultaneous offset beams. The phase relationship between the signals in the 
offset beams is not used. The purpose of the phase-sensitive detector is to conveniently 
furnish the sign of the error signal. 

A block diagram of a monopulse radar with provision for extracting error signals in 
both elevation and azimuth is shown in Fig. 5.10. The cluster of four feeds generates 
four partially overlapping antenna beams. The feeds might be used with either a 
parabolic reflector or a lens. All four feeds generate the sum pattern. The difference 
pattern in one plane is formed by taking the sum of two adjacent feeds and subtracting 
this from the sum of the other two adjacent feeds. The difference pattern in theorthog- 
onal plane is obtained by adding the differences of the orthogonal adjacent pairs. A 



178 



Introduction to Radar Systems 



[Sec. 5.4 



total of four hybrid junctions generate the sum channel, the azimuth difference channel, 
and the elevation difference channel. Three separate mixers and IF amplifiers are 
shown, one for each channel. All three mixers operate from a single local oscillator in 
order to maintain the phase relationships between the three channels. Two phase- 
sensitive detectors extract the angle-error information, one for azimuth, the other for 
elevation. Range information is extracted from the output of the sum channel after 
amplitude detection. 

Since a phase comparison is made between the output of the sum channel and each of 
the difference channels, it is important that the phase shifts introduced by each of the 
channels be almost identical. According to Page, 13 the phase difference between 
channels must be maintained to within 25° or better for reasonably proper performance. 
The gains of the channels also must not differ by more than specified amounts. 




M^rj— o^litier} ^ 



Amplitude 
detector 



Video 
amplifier 



- Range 



Phase-sensitive 
detector 



IF 
amplifier 



Phase -sensitive 
detector 



Elevation- 
■ angle 
error 



Azimuth- 
angle 
error 



LO 



Fig. 5.10. Block diagram of two-coordinate (azimuth and elevation) amplitude-comparison-mono- 
pulse tracking radar. 

An alternative approach to using three identical amplifiers in the monopulse receiver 
is to use but one IF channel which amplifies the sum signal and the two difference 
signals on a time-shared basis. 17 - 19 The sum signal is passed through the single IF 
amplifier followed by the two difference signals delayed in time by a suitable amount. 
Most of the gain and gain control take place in the single IF amplifier. Any variations 
affect all three signals simultaneously. After amplification, compensating delays are 
introduced to unscramble the time sequence and bring the sum signal and the two 
difference signals in time coincidence. Phase detection occurs as in the conventional 
monopulse. It is claimed that the phase and gain between channels have been main- 
tained to within ±2.5° and ±| db, respectively, with this technique. 19 

Monopulse Error Signal. Assume that the antenna pattern is represented by the 
Gaussian function. The one-way (voltage) pattern from one monopulse beam is 
Gl exp (— aWjl), where G is the maximum antenna gain, a % = 2.776/0|, and 6% is the 
antenna beamwidth as measured between the half-power points. The angular separa- 
tion between the two antenna beams is 20 a , and the angle between the target and the axis 
of symmetry is T . Assuming no mutual coupling between the two feed horns, the 
one-way (voltage) sum pattern is 



2Gq exp 


-| (0* + (?*,) 


The one-way (voltage) difference pattern is 


2G\ exp 


- a - (e; + 0§o 



cosh a 2 6 Q 6 T 



sinh a 2 d a d,, 



(5.18) 



(5.19) 



Sec. 5.4] Tracking Radar 179 

The IF voltage produced by the difference signal will be proportional to the product of 
Eqs. (5.18) and (5.19). 

IF difference signal (voltage) = 2Kexp [—a 2 (d\ + 0|)] 

X sinh 2a 2 d q 6 T cos 2-rrf IF t (5.20) 

where A' is a constant determined by the parameters of the radar equation. 

The two-way (voltage) antenna pattern for the sum channel is the square of Eq. (5. 1 8). 
The sum and difference signals [Eq. (5.20)] are multiplied in the phase-sensitive detector 
to give the error signal. The output of the phase-sensitive detector is a d-c voltage 
whose amplitude is proportional to the product of the sum and difference amplitudes, 
or 

Error signal = c x exp \_-2a 2 (6 2 q + #§,)] cosh 2 a 2 6 q 6 T sinh 2a 2 6 q 6 T (5.21) 

For small angular errors this reduces to 

Error signal = c 2 6 T (5.22) 

where c x and c 2 are constants. Thus the error signal in the monopulse radar is a linear 
function of the angular displacement of the target from the axis, assuming small angular 
displacements. 

Comparison of Monopulse and Conical-scan Error Signals. The greater the signal-to- 
noise ratio and the steeper the slope of the error signal in the vicinity of zero angular 
error, the more accurate is the measurement of angle. The slopes of the error signal at 
crossover in the monopulse, the conical-scan tracker, and a tracker which operates on 
the difference patterns only will be compared and used as a basis for relative accuracy. 

The receiver is assumed to be linear, an assumption which should have little effect on 
the conclusions, especially for large signal-to-noise ratios. This is usually the case if 
accurate measurements are to be obtained. The one-way (voltage) antenna pattern is 
represented analytically by the Gaussian function exp (—a 2 6 2 /2), where the constant 
a 2 = 2.176/6%, and the antenna gain is normalized; that is, G ~\. The one-way 
(voltage) sum pattern in the monopulse radar is [from Eq. (5.18)] 



2 exp 



"-{61 + 6%) 



cosh a 2 6 q 6 T (5.23) 



where 6 q and d T are defined as before. The one-way (voltage) difference pattern 
[Eq. (5.19)] is 



2 exp 



L -f(^ 2 +6 2 r) 



sinh a 2 6 q 6 T (5.24) 



The monopulse error signal is [Eq. (5.21) with q = 4] 

V m = 4 exp [-2a 2 (6 2 + d%)~] cosh 2 a 2 6 Q Q T sinh 2a\6 T (5.25) 

The error signal in the lobe-switching or the conical-scan radar (in one coordinate) is 
proportional to the difference of the two-way (voltage) antenna pattern exp (—aW). 

V c = 2 exp \_-a\6 2 a + 0|,)] sinh 2a 2 6 Q d T (5.26) 

In a radar which transmits and receives on the difference pattern only, the error signal 
is 

V„ = 4 exp [-a\d 2 q + d 2 T )~] sinh 2 a 2 6 q 6 r (5.27) 



180 Introduction to Radar Systems [Sec. 5.4 

The slopes of these three error signals (V m , V e , and V d ) evaluated at 6 T = are 



Monopulse 
Conical scan 
Difference pattern 



te\ =8a 2 e 9 exp(-2« 2 ^) 
\au T le T =o 

te) =4a 2 e a exp(-a^) 
\aO T h T =o 

(&) =0 

\dd T 'e T =o 



(5.28) 
(5.29) 
(5.30) 



A radar which utilizes the difference pattern for both transmitting and receiving does 
not have as suitable an error signal as the other two radars since its slope is zero for 
6 T = 0. The error-signal slope of the monopulse radar is slightly greater than the 



5.0 




Squint angle B q /6s 
0.10.2 0.3 0.4 0.5 0.6 

0^ h \ 1 r- 1 - 



0.7 
L, 



1 2 3 4 5 6 

Beam crossover, db 

Fig. 5.11. Slope of the angular-error signal at crossover for monopulse and conical-scan tracking 
radars (fi B = half-power beamwidth, 0„ = squint angle). 

slope of the conical-scan radar error signal over the range of squint-angle values of 
practical interest. This is illustrated in Fig. 5.11. The ordinate is the product of the 
error-signal slope times the antenna beamwidth, and the abscissa is shown as either the 
squint angle or the crossover point of the antenna patterns. The maximum slope of 
the conical-scan radar occurs at a crossover of 2.2 db. The crossover values of 
practical conical-scan radars are usually in this vicinity. The maximum of the curve is 
rather broad, with some leeway allowed in the selection of the optimum. The greater 
the crossover level, however, the less will be the signal-to-noise ratio when the target is 
directly on axis. The maximum slope of the monopulse radar is seen to occur at a beam 
crossover of approximately 1 . 1 db. 

In general, it is more difficult to achieve a low crossover with practical monopulse 
antennas than with conical-scan antennas. The monopulse radar usually generates its 
two (or four) overlapping beams from two (or four) adjacent feed horns. Since there is 
a physical limit to the minimum spacing between the feed horns, there will be a corre- 
spondingly lower limit to the separation between the two monopulse beams. However, 
Fig. 5.1 1 indicates that the jc/pssover can be much greater than the optimum and still 
result in a slope as high as %e?56onical-scan slope. Therefore the slope of the error 
signals in practical conical-scan'and monopulse tracking radars will be comparable if 
the antenna pattern is the only factor of consequence. It should also be noted that 



Sec. 5.4] 



Tracking Radar 



181 




Target 



since the ordinate in Fig. 5.11 is the product of the slope times the beamwidth, the 
smaller the beamwidth of the antenna, the larger will be the slope and the better 
the tracking accuracy. A word of caution should be given concerning the nature of 
the Gaussian approximation to the antenna beam shape assumed above. In actual 
practice the sum (or difference) pattern may not be the sum (or difference) of the two 
overlapping offset patterns. There will usually be some interaction between the two 
feed horns which can alter the two patterns. 20 ' 21 

Phase-comparison Monopulse. The tracking techniques discussed thus far in this 
chapter were based on a comparison of the amplitudes of echo signals received from two 
or more antenna positions. The sequential-lobing and conical-scan techniques used a 
single, time-shared antenna beam, while the monopulse technique used two or more 
simultaneous beams. The difference in amplitudes in the several antenna positions was 
proportional to the angular error. The angle of 
arrival (in one coordinate) may also be deter- 
mined by comparing the phase difference between 
the signals from two separate antennas. Unlike 
the antennas of amplitude-comparison trackers, 
those used in phase-comparison systems are not 
offset from the axis. The individual boresight 
axes of the antennas are parallel, causing the 
(far-field) radiation to illuminate the same 
volume in space. The amplitudes of the target 
echo signals are essentially the same from each 
antenna beam, but the phases are different. 

The measurement of angle of arrival by com- 
parison of the phase relationships in the signals 
from the separated antennas of a radio inter- 
ferometer has been widely used by the radio 
astronomers for precise measurements of the 
positions of radio stars. The interferometer as 
used by the radio astronomer is a passive instru- 
ment, the source of energy being radiated by the 
target itself. A tracking radar which operates with phase information is similar to an 
active interferometer and might be called an interferometer radar. It has also been 
called simultaneous-phase-comparison radar, or phase-comparison monopulse. The 
latter term is the one which will be used here. 

In Fig. 5.12 two antennas are shown separated by a distance d. The distance to the 
target is R and is assumed large compared with the antenna separation d. The line of 
sight to the target makes an angle 6 to the perpendicular bisector of the line joining the 
two antennas. The distance from antenna 1 to the target is 



Antenna 
No.1 



Fig. 5.12. Wavefront phase relationships 
in phase-comparison-monopulse radar. 



R x = R + - sin i 



and the distance from antenna 2 to the target is 



sin 6 



The phase difference between the echo signals in the two antennas is approximately 

A<£ = — dsind (5.31) 

A 



182 Introduction to Radar Systems 



[Sec. 5.4 



For small angles where sin 6 «* 0, the phase difference is a linear function of the angular 
error and may be used to position the antenna via a servo-control loop. 

A block diagram of a phase-comparison monopulse 22 in one angular coordinate is 
shown in Fig. 5.13. Two antennas are shown side by side. These are directive 
antennas, one of which is connected to the transmitter and receiver as in a conventional 
radar, while the other antenna feeds a receiver only. The transmitter is shown con- 
nected to the antenna via a duplexer. In practice, a second duplexer might be inserted 
in front of the other receiver, not so much for protection, but to balance the phase shifts 
in the two channels. The two receiving channels should be identical. The RF echo 
signals are heterodyned to an intermediate frequency with a common local oscillator. 
The outputs of the two IF amplifiers are compared in a phase detector whose output is 
a voltage proportional to A</> of Eq. (5.31). This voltage is used as the error-signal 
input to a servo-control loop which positions the antenna to make the error signal zero. 
One of the receiving channels is envelope-detected, as in the normal radar receiver, to 
extract the range information. 




Radiation patterns 



Mixer 



IF 
amplifier 



Local 
oscillator 



Duplexer 



Transmitter 



Mixer 





Phase 
detector 


















IF 
amplifier 






Envelope 
detector 











Angle-error 
information 



^_ Range 
information 



Fig. 5.13. Block diagram of phase-comparison-monopulse radar (one angular coordinate). 



An additional antenna and receiving channel is necessary in order to track in two 
orthogonal coordinates. In one implementation of the phase-comparison monopulse 
radar, 22 four antennas were arranged in a square to obtain tracking in both elevation 
and azimuth. One of these antennas was a transmitter only, while the other three were 
receivers. One antenna was connected to the elevation receiver, another to the azimuth 
receiver, and one to a common receiver which supplied the reference for both the 
elevation and azimuth receiver. Instead of obtaining the error signal from a phase 
comparison (as in Fig. 5.13), the sum and difference signals may be derived (as in the 
amplitude-comparison monopulse) and compared in a phase-sensitive detector. 16 

Although tracking radars based upon the phase-comparison principle have been 
built and found to track aircraft satisfactorily, this technique has not been as widely 
used as some of the others discussed. There are two reasons why this might be so. 
First, the sidelobe levels which result can sometimes be higher than those from a single 
reflector, and second, the phase comparison radar does not usually make efficient use of 
the total available antenna aperture. These two points are elaborated upon below. 

When two omnidirectional antennas are separated by distances of many wavelengths, 
as are the separations in the phase-comparison monopulse, a multilobed pattern will 
be formed. The lobes of the pattern are called grating lobes, by analogy with the 
optical diffraction grating. They have also been called principal maxima. Each of the 
grating lobes of the pattern will be of the same amplitude. The positions of the grating 
lobes may be found by setting Aci = 2nn in Eq. (5.31) (where n is an integer) and 
solving for d. The main lobe corresponds to n = 0. The grating lobes appear when 
n ^ and result in an ambiguous angle measurement. Many of the grating lobes will 
be suppressed if directive antenna elements are used rather than the omnidirectional 



Sec. 5.4] Tracking Radar 183 

elements assumed in the above illustration. The element pattern multiplies the 
interference pattern of the two separated omnidirectional elements, with the result that 
those lobes outside the coverage of the element pattern will be reduced. In other words, 
the resultant pattern is the product of the element pattern times the array pattern. 
The directivity of the element pattern will tend to reduce the magnitude of the grating 
lobes, but in general, the reduction will not be as complete as might be desired. 

As an example of the positions of the grating lobes relative to the element pattern, 
assume that the antenna-reflector size is 30 wavelengths in diameter and that the 
separation between the antennas is also 30 wavelengths ; that is, the two antennas are 
just touching. The first grating lobe [n = 1 or A</> = 2n radians in Eq. (5.31)] will 
occur at 6 = ±1.9°, and the second grating lobe at d = ±3.8°. Assuming that the 
half-power beamwidth of the element pattern is given by d B = 65A/D, where DjX = 30, 
the half-power points correspond to 6 = ± 1 .09°. As a rough rule of thumb, the first 
null for parabolic-reflector antennas occurs at approximately ±1.2 B = ±2.65°, 
and the first sidelobe approximately half a beamwidth farther, or ±3.74°. Therefore 
we see that the position of the first grating lobe lies between the half-power point and 
the first null. Depending upon its exact location, it may either widen the main lobe or 
create a shoulder lobe, or even a pronounced sidelobe. The second grating lobe occurs 
in the vicinity of the first sidelobe of the element pattern, with the likelihood that the 
first sidelobe level will be raised. 

One limitation of the phase-comparison-monopulse tracker described in Fig. 5.13 is 
that it does not use its available antenna aperture as efficiently as other types of tracking 
radars. For example, suppose that four parabolic reflectors were used to achieve 
tracking in two coordinates, with one antenna for transmission and the other three for 
reception. The effective antenna area (or the gain) that is substituted into the radar 
equation is that of one of the antennas, not that of all four together. Therefore, if an 
amplitude-comparison-monopulse antenna or a conical-scan antenna occupied the 
same area as the four antennas, its effective aperture might be as much as four times 
greater than if it were used with the type of phase-comparison monopulse shown in 
Fig. 5.13. A factor of 4 in the effective antenna area can result in a factor-of-2 change 
in range. 

Both the amplitude-comparison-monopulse and the phase-comparison-monopulse 
trackers employ two antenna beams (for one coordinate tracking). The measurements 
made by the two systems are not the same; consequently, the characteristics of the 
antenna beams will also be different. In the amplitude-comparison monopulse the two 
beams are offset, that is, point in slightly different directions. This type of pattern may 
be generated by using one reflector dish with two feed horns side by side (four feed horns 
for two coordinate data). Since the feeds may be placed side by side, they could be as 
close as one-half wavelength. With such close spacing the phase difference between 
the signals received in the two feeds is negligibly small. Any difference in the amplitudes 
between the two antenna outputs in the amplitude-comparison system is a result of 
differences in amplitude and not phase. The phase-comparison monopulse, on the 
other hand, measures phase differences only and is not concerned with amplitude 
difference. Therefore the antenna beams are not offset, but are directed to illuminate a 
common volume in space. Separate antennas are needed since it is difficult to illumi- 
nate a single reflector with more than one feed and produce independent antenna 
patterns which illuminate the same volume in space. 

The phase-comparison-monopulse tracking radar described above is but one method 
of employing phase information. In one embodiment of the phase-comparison 
principle as applied to missile guidance the phase difference between the signals in two 
fixed antennas is measured with a servo-controlled phase shifter located in one of the 
arms. 33 The servo loop adjusts the phase shifter until the difference in phase between 



184 Introduction to Radar Systems [Sec. 5.5 

the two channels is a null. The amount of phase shift which has to be introduced to 
make a null signal is a measure of the angular error. 

The phase- and amplitude-comparison principles can be combined in a single radar 
to produce two-dimensional angle tracking with only two, rather than four, antenna 
beams. 17 The angle information in one plane (the azimuth) is obtained by two separate 
antennas placed side by side as in a phase-comparison monopulse. One of the beams 
is tilted slightly upward, while the other is tilted slightly downward, to achieve the squint 
needed for amplitude-comparison monopulse in elevation. Therefore the horizontal 
projection of the antenna patterns is that of a phase-comparison system, while the 
vertical projection is that of an amplitude-comparison system. 

5.5. Target-reflection Characteristics and Angular Accuracy 

The angular accuracy of tracking radar will be influenced by such factors as the 
mechanical properties of the radar antenna and pedestal, the method by which 
the angular position of the antenna is measured, the quality of the servo system, the 
stability of the electronic circuits, the noise level of the receiver, the antenna beam width, 
atmospheric fluctuations, and the reflection characteristics of the target. These factors 
can degrade the tracking accuracy by causing the antenna beam to fluctuate in a random 
manner about the true target path. These noiselike fluctuations are sometimes called 
tracking noise, or jitter. In many cases the two factors which ultimately limit the 
angular accuracy of practical tracking radars are the mechanical errors and the target- 
reflectivity characteristics. The mechanical errors associated with tracking radars will 
not be discussed here. (An example of the mechanical errors experienced in a precise 
monopulse tracking radar, the AN/FPS-16, has been described by Barton. 24 - 25 ) 

A simple radar target such as a smooth sphere will not cause degradation of the 
angular-tracking accuracy. The radar cross section of a sphere is independent of 
the aspect at which it is viewed ; consequently, its echo will not fluctuate with time. The 
same is true, in general, of a radar beacon if its antenna pattern is omnidirectional. 
However, most radar targets are of a more complex nature than the sphere. The 
amplitude of the echo signal from a complex target may vary over wide limits as the 
aspect changes with respect to the radar. In addition, the effective center of radar 
reflection may also change. Both of these effects — amplitude fluctuations and wander- 
ing of the radar center of reflection — as well as the limitation imposed by receiver noise 
can limit the tracking accuracy. These effects are discussed below. 

Amplitude Fluctuations. A complex target such as an aircraft or a ship may be 
considered as a number of independent scattering elements. The echo signal can be 
represented as the vector addition of the contributions from the individual scatterers. 
If the target aspect changes with respect to the radar — as might occur because of motion 
of the target, or turbulence in the case of aircraft targets — the relative phase and 
amplitude relationships of the contributions from the individual scatterers also change. 
Consequently, the vector sum, and therefore the amplitude, change with changing target 
aspect. 

Amplitude fluctuations of the echo signal are important in the design of the lobe- 
switching radar and the conical-scan radar but are of little consequence to the mono- 
pulse tracker. Both the conical-scan tracker and the lobe-switching tracker require a 
finite time to obtain a measurement of the angle error. This time corresponds in the 
conical-scan tracker to at least one revolution of the antenna beam. With lobe 
switching, the minimum time is that necessary to obtain echoes at the four successive 
angular positions. In either case a minimum of four pulse-repetition periods are 
required to make a measurement; in practice, many more than four are often used. If 
the target cross section were to vary during this observation time, the change might be 
erroneously interpreted as an angular-error signal. The monopulse radar, on the 



Sec. 5.5] Tracking Radar 185 

other hand, determines the angular error on the basis of a single pulse. Its accuracy 
will therefore not be affected by changes in amplitude with time. 

The echo signal from complex targets is best described in statistical terms. Some of 
the more useful statistical descriptions that have been applied to cross sections are the 
cumulative probability distribution, the autocorrelation function, and the power 
spectral density. The power-spectral-density function is useful for describing the 
effect of amplitude fluctuations on the performance of a conical-scan or lobe-switching 
tracker. 

A typical power spectrum of the target amplitude fluctuations (fading) with a 
conical-scan tracking radar might appear as in Fig. 5.14. This curve is an analytical 
approximation to the experimental spectrum derived from 30 sec of azimuth data 



T — I — I — I — r 



i — r 




n — i — i — r 



12 
Frequency, cps 



1 — I- 



18 20 



Fig. 5.14. Power spectral density of amplitude fluctuations for a C-47 aircraft on a crossover course. 
(Courtesy J. E. Ward and the MIT Servomechanism Laboratory. 42 ) 

obtained from a radar tracking a C-47 aircraft flying a crossover course. 42 The 
minimum range was 300 yd, and the maximum range was 5,000 yd. The autocorrela- 
tion function (which is the Fourier cosine transform of the power spectrum) corre- 
sponding to the spectrum of Fig. 5.14 is <f>(r) = 1,410 exp (— 16.6t), where <f(r) is in 
units of square mils. For a radial trajectory over the same range limits the auto- 
correlation function is </>(t) = 40 exp (— 13t). 

To reduce the effect of amplitude noise on tracking, the conical-scan frequency should 
be chosen to correspond to a low value of amplitude noise. If considerable amplitude 
fluctuation noise were to appear at the conical-scan or lobe-switching frequencies, it 
could not be readily eliminated with filters or AGC. A typical scan frequency might be 
of the order of 30 cps. Higher frequencies might also be used since target amplitude 
noise generally decreases with increasing frequency. However, this may not always be 
true. Propeller-driven aircraft produce modulation components at the blade frequency 
and harmonics thereof and can cause a substantial increase in the spectral energy 
density at certain frequencies. 43 Also, the scan frequency cannot be made higher than 
one-quarter the pulse repetition frequency if a minimum of one hit per quadrant is to be 
obtained. It has been found experimentally that the tracking accuracy of radars 
operating with pulse repetition frequencies from 1,000 to 4,000 cps and a lobing or 
scan rate one-quarter of the prf are not limited by echo amplitude fluctuations. 26 



186 Introduction to Radar Systems [Sec. 5.5 

The percentage modulation of the echo signal due to cross-section amplitude fluctua- 
tions is independent of range if AGC is used. Consequently, the angular error as a 
result of amplitude fluctuations will also be independent of range. 

Angle Fluctuations. 2 ^ 32 Changes in the target aspect with respect to the radar can 
cause the apparent center of radar reflections to wander from one point to another. 
(The apparent center of radar reflection is the direction of the antenna when the error 
signal is zero.) In general, the apparent center of reflection might not correspond to 
the target center. In fact, it need not be confined to the physical extent of the target and 
may be off the target a significant fraction of the time. The random wandering of the 
apparent radar reflecting center gives rise to noisy or jittered angle tracking. This form 
of tracking noise is called angle noise, angle scintillations, angle fluctuations, or target 
glint. The angular fluctuations produced by small targets at long range may be of 
little consequence in most instances. However, at short range or with relatively large 
targets (as might be seen by a radar seeker on a homing missile), angular fluctuations 
may be the chief factor limiting tracking accuracy. Angle fluctuations affect all 
tracking radars whether conical-scan, sequential-lobing, or monopulse. 

Consider a rather simplified model of a complex radar target consisting of two 
independent isotropic scatterers separated by an angular distance d D , as measured from 
the radar. Although such a target may be fictitious and used for reasons of mathe- 
matical simplicity, it might approximate a target such as a small fighter aircraft with 
wing-tip tanks or two aircraft targets flying in formation and located within the same 
radar resolution cell. It is also a close approximation to the low-angle tracking 
problem in which the radar sees the target plus its image reflected from the surface. 
The qualitative effects of target glint may be assessed from this model. The relative, 
amplitude between the cross sections of the two scatterers is assumed to be a, and the 
relative phase difference is a. Differences in phase might be due to differences in range 
or to reflecting properties. The cross-section ratio a is defined as a number less than 
unity. The angular error A0 as measured from the larger of the two targets is 27 

— — Q 2 + a cos <x 
D 1 + a 2 ■+ 2a cos a 

This is plotted in Fig. 5.15. The position of the larger of the two scatterers corresponds 
to A0/0Q = 0, while the smaller-scatterer position is at A0/0 7J = + 1 . Positive values 
of AS correspond to an apparent radar center which lies between the two scatterers; 
negative values lie outside the target. When the echo signals from both scatterers are 
in phase (a = 0), the error reduces to a/(a + 1), which corresponds to the so-called 
"center of gravity" of the two scatterers (not to be confused with the mechanical center 
of gravity). 

Angle fluctuations are due to random changes in the relative distance from radar to 
the scatterers, that is, varying values of a. These changes may result from turbulence 
in the aircraft flight path or from the changing aspect caused by target motion. In 
essence, angle fluctuations are a distortion of the phase front of the echo signal reflected 
from a complex target and may be visualized as the apparent tilt of this phase front as it 
arrives at the tracking system. 

Equation (5.32) indicates that the tracking error A6 due to glint for the two-scatterer 
target is directly proportional to the angular extent of the target Q D . This is probably a 
reasonable approximation to the behavior of real targets, provided the angular extent 
of the target is not too large compared with the antenna beamwidth. Since Q D varies 
inversely with distance for a fixed target size, the tracking error due to glint also varies 
inversely with distance. 

A slightly more complex model than the two-scatterer target considered above is one 
consisting of many individual scatterers, each of the same cross section, arranged 



Sec. 5.5] 



Tracking Radar 187 



uniformly along a line of length L perpendicular to the line of sight from the radar. The 
resultant cross section from such a target is assumed to behave according to the Rayleigh 
probability distribution. The probability of the apparent radar center lying outside 
the angular region of LjR radians (in one tracking plane) is 0. 1 34, where R is the 
distance to the target. 28 Thus 13.4 per cent of the time the radar will not be directed to 
a point on the target. Similar results for a two-dimensional model consisting of 
equal-cross-section scatterers uniformly spaced over a circular area indicate that the 
probability that the apparent radar center lies outside this target is 0.20. 

Angle fluctuations in a tracking radar are reduced by increasing the time constant of 
the AGC system (reducing the bandwidth). 26 - 33 ' 34 However, this reduction in angle 
fluctuation is accompanied by a new component of noise caused by the amplitude 
fluctuations associated with the echo signal; that is, narrowing the AGC bandwidth 




20 



40 



60 80 100 120 
Phase difference ex 



140 160 180 



Fig. 5.15. Plot of Eq. (5.32). Apparent radar center A0 of two isotropic scatterers of relative 
amplitude a and relative phase shift a, separated by an angular extent 6 D . 

generates additional noise in the vicinity of zero frequency, and poorer tracking results. 
Amplitude noise modulates the tracking-error signals and produces a new noise 
component, proportional to true tracking errors, that is enhanced with a slow AGC. 
Under practical tracking conditions it seems that a wide-bandwidth (short-time 
constant) AGC should be used to minimize the over-all tracking noise. However, the 
servo bandwidth should be kept to a minimum consistent with tactical requirements in 
order to minimize the noise. 

Receiver and Servo Noise. Another limitation on tracking accuracy is the receiver 
noise power. The accuracy of the angle measurement is inversely proportional to the 
square root of the signal-to-noise power ratio. 35 Since the signal-to-noise ratio is 
proportional to l/# 4 (from the radar equation), the angular error due to receiver noise 
is proportional to the square of the target distance. 

Servo noise is the hunting action of the tracking servomechanism which results from 
backlash and compliance in the gears, shafts, and structures of the mount. The 
magnitude of servo noise is essentially independent of the target echo and will therefore 
be independent of range. 26 ' 33 

Summary of Errors. The contributions of the various factors affecting the tracking 
error are summarized in Fig. 5.16. Angle-fluctuation noise varies inversely with range ; 
receiver noise varies as the square of the range; and amplitude fluctuations and servo 
noise are independent of range. This is a qualitative plot showing the gross effects of 



188 Introduction to Radar Systems [Sec. 5.5 

each of the factors. Two different resultant curves are shown. Curve A is the sum of 
all effects and is representative of conical-scan and sequential-lobing tracking radars. 
Curve B does not include the amplitude fluctuations and is therefore representative of 
monopulse radars. In Fig. 5. 1 6 the amplitude fluctuations are assumed to be larger 
than servo noise. If not, the improvement of monopulse tracking over conical scan 
will be negligible. In general, the tracking accuracy deteriorates at both short and long 
target ranges, with the best tracking occurring at some intermediate range. 



E 
$0.01 





1 1 1 1 1 1 1 1 1 


1 


1 1 1 1 hi i i 


1 1 1 1 1 l 


- 






1 / 


- 


— 




© ^ 


/° 

h 

// Amplitude 


— 




^y. 


/ fluctuations 
Servo noise 


'^ 


- 


1 1 1 1 1 1 III 


i i 


i I i I nl I i 


1 1 1 II 



10 100 

Relative radar range 



1,000 



Fig. 5.16. Relative contributions to angular tracking error due to amplitude fluctuations, angle 
fluctuations, receiver noise, and servo noise as a function of range. (A) Composite error for a conical- 
scan or sequential-lobing radar; (B) composite error for monopulse. 

At sufficiently long ranges, the signal-to-noise ratio may be too low to permit satis- 
factory tracking and the radar "loses track." Swerling analyzed the effect of receiver 
noise on the tracking performance using the loss rate as a criterion of performance, 
defined as the expected number of times per second the tracking error (in either range or 
angle) exceeds the maximum allowable value. 36 The loss rate can serve as a criterion 
to find an optimum choice of servo parameters, transmitter power, maximum range, 
and other similar tracking-radar parameters. Swerling's analysis applies to either 
monopulse angle tracking or split-range-gate tracking (described in the next section). 
Three of the formulas derived by Swerling are presented below (in his notation). 

The output signal-to-noise (power) ratio Y versus loss rate A is 



( Kt Y( 1 Vln° 5/c 
\2dJ ll - 5/6 J n A 



(5.33) 



where K = a correction factor of order of unity and accounts for type of tracking- 
error circuit employed, distortion of pulse in IF, and particular type of 
linear approximation used instead of actual error vs. voltage curve 
t = width between two-way half-power points of each beam (angle tracking) 
or width of each range gate (range tracking) 
S m = maximum allowable tracking error 
3 = average tracking error 

f e = equivalent square-band cutoff frequency of the servo regarded as an audio 
filter 



Sec 56] Tracking Radar 189 

The relationship between the output signal-to-noise ratio Y and the IF signal-to-noise 
ratio X for square-law detection is 

y=J^ (5.34) 

1 +2X 

where Nis the effective number of pulses integrated by the servo and is equal to the IF 
bandwidth divided by 2f c . The variance of the tracking error is 

o\ « ^ (5.35) 

87 

This is consistent with the form of the theoretical errors derived in Chap. 10 for 
other radar measurements. The greater the beamwidth (or the pulse width), the 
poorer will be the angle (or the range) accuracy. The rms tracking error (square 
root of the variance) is inversely proportional to the square root of the signal-to-noise 
ratio. 

5.6. Tracking in Range 

In most tracking-radar applications the target is continuously tracked in range as well 
as in angle. Range tracking might be accomplished by a human operator who watches 
an A-scope or J-scope presentation and manually positions a handwheel in order to 
maintain a marker over the desired target pip. The setting of the handwheel is a 
measure of the target range and may be converted to a voltage that is supplied to a data 
processor. The data processor in a fire-control radar predicts the future position of 
the target for the purpose of aiming the weapon. 

The human operator tracking a target by positioning a handwheel can be considered 
as part of a servo loop. 1 In pure displacement tracking, the turns of the handwheel are 
made proportional to the displacement of the target. If the target's range changes at a 
constant rate, the operator must turn his handwheel at a constant rate. If he is lagging 
behind the target, he will turn faster until the error is corrected ; if he is leading the 
target, he will turn more slowly. In pure rate tracking, the position of the handwheel 
determines the speed at which the movable marker on the CRT follows the target pip. 
When tracking a target moving with constant velocity the handwheel need not be turned 
once the proper adjustment has been made. 

Displacement and rate tracking may be combined so that the handwheel position 
automatically corrects for speed at the same time that the displacement error is corrected. 
This is called aided tracking. Aided tracking may also be used for manual tracking in 
angle as well as range. 

As target speeds increase, it is increasingly difficult for an operator to perform at the 
necessary levels of efficiency over a sustained period of time, and automatic tracking 
becomes a necessity. Indeed, there are many tracking applications where an operator 
has no place, as in a homing missile or in a small space vehicle. 

The technique for automatically tracking in range is based on the split range gate.f 
Two range gates are generated as shown in Fig. 5.17. One is the early gate, and the 
other is the late gate. The echo pulse is shown in Fig. 5.17a, the relative position of 
the gates at a particular instant in Fig. 5.176, and the error signal in Fig. 5.17c. The 
portion of the signal energy contained in the early gate is less than that in the late gate. 
If the outputs of the two gates are subtracted, an error signal (Fig. 5.17c) will result 
which may be used to reposition the center of the gates. 37 The magnitude of the error 
signal is a measure of the difference between the center of the pulse and the center of the 

t Gating is the process of selecting those portions of a wave which exist during one or more selected 
time intervals (IRE definition"). 



190 



Introduction to Radar Systems 



[Sec. 5.7 



gates. The sign of the error signal determines the direction in which the gates must be 
repositioned by a feedback-control system. When the error signal is zero, the range 
gates are centered on the pulse. 

The range gating necessary to perform automatic tracking offers several advantages 
as by-products. It isolates one target, excluding targets at other ranges. This permits 
the boxcar generator to be employed. Also, range gating improves the signal-to-noise 
ratio since it eliminates the noise from the other range intervals. Hence the width of 
the gate should be sufficiently narrow to minimize extraneous noise. On the other 
hand, it must not be so narrow that an appreciable fraction of the signal energy is 
excluded. A reasonable compromise is to make the gate width of the order of the 
pulse width. 

Echo j pulse 



U) 




/ 


n 
















Time — > 


(i>) 




Early 
gate 


Late 
gate 






(c) 


Early gate I 
signal / 


Time — *• 








/ 


Late gate 
signal 


Time — *■ 



Fig. 5.17. Split-range-gate tracking, 
between early and late range gates. 



(a) Echo pulse; (b) early-late range gates; (c) difference signal 



A target of finite length can cause noise in range-tracking circuits in an analogous 
manner to angle-fluctuation noise (glint) in the angle-tracking circuits. Range- 
tracking noise depends on the length of the target and its shape. It has been reported 26 
that the rms value of the range noise is approximately 0.8 of the target length when 
tracking is accomplished with a video split-range-gate error detector. 

5.7. Tracking in Doppler 

Tracking radars designed to extract doppler information, such as the CW or the 
pulse-doppler tracking radars, can also track the doppler frequency shift. This may be 
accomplished with a frequency discriminator and a tunable oscillator. Other tech- 
niques are, of course, possible. 44 Tracking the doppler frequency shift with a narrow- 
band doppler filter (one which is wide enough to encompass the frequency spectrum 
occupied by the signal energy) offers two advantages: (1) the signal-to-noise ratio is 
improved, especially if the doppler frequency shift is large compared with the informa- 
tion bandwidth of the received signal; and (2) it may be used to resolve a desired target 
from a group of targets, especially in CW or pulse-doppler tracking radars. 

5.8. Acquisition 

A tracking radar must first find and acquire its target before it can operate as a tracker. 
Therefore it is usually necessary for the radar to scan an angular sector in which 
the presence of the target is suspected. Most tracking radars employ a narrow pencil- 
beam antenna. Searching a volume in space for an aircraft target with a narrow pencil 
beam would be somewhat analogous to searching for a fly in a darkened auditorium 
with a flashlight. It must be done with some care if the entire volume is to be covered 



Sec. 5.8] Tracking Radar 191 

uniformly and efficiently. Examples of the common types of scanning patterns em- 
ployed with pencil-beam antennas are illustrated in Fig. 5.18. 

In the helical scan, the antenna is continuously rotated in azimuth while it is simultane- 
ously raised or lowered in elevation. It traces a helix in space. Helical scanning was 
employed for the search mode of the SCR-584 fire-control radar, developed during 
World War II for the aiming of antiaircraft-gun batteries. 38 The SCR-584 antenna 
was rotated at the rate of 6 rpm and covered a 20° elevation angle in 1 min. The Palmer 
scan derives its name from the familiar penmanship exercises of grammar school days. 
It consists of a rapid circular scan (conical scan) about the axis of the antenna, combined 
with a linear movement of the axis of rotation. When the axis of rotation is held 
stationary, the Palmer scan reduces to the conical scan. Because of this property, the 
Palmer scan is sometimes used with conical-scan tracking radars which must operate 
with a search as well as a track mode since the same mechanisms used to produce conical 
scanning can also be used for Palmer scanning. 39 Some conical-scan tracking radars 
increase the squint angle during search in order to reduce the time required to scan a 
given volume. The conical scan of the SCR-584 was operated during the search mode 
and was actually a Palmer scan in a helix. In general, conical scan is performed during 
the search mode of most tracking radars. 

The Palmer scan is suited to a search area which is larger in one dimension than 
another. The spiral scan covers an angular search volume with circular symmetry. 
Both the spiral scan and the Palmer scan suffer from the disadvantage that all parts of 
the scan volume do not receive the same energy unless the scanning speed is varied during 
the scan cycle. As a consequence, the number of hits returned from a target when 
searching with a constant scanning rate depends upon the position of the target within 
the search area. 




(/>) U) 



=P 




(d) (e) 

Fig. 5.18. Examples of acquisition search patterns, (a) Trace of helical scanning beam; (b) Palmer 
scan; (c) spiral scan; (d) raster, or TV, scan; (e) nodding scan. 

The raster, or TV, scan, unlike the Palmer or the spiral scan, paints the search area 
in a uniform manner. The raster scan is a simple and convenient means for searching 
a limited sector, rectangular in shape. Similar to the raster scan is the nodding scan 
produced by oscillating the antenna beam rapidly in elevation and slowly in azimuth. 
Although it may be employed to cover a limited sector — as does the raster scan — 
nodding scan may also be used to obtain hemispherical coverage, that is, elevation 
angle extending to 90° and the azimuth scan angle to 360°. 

The helical scan and the nodding scan can both be used to obtain hemispheric 
coverage with a pencil beam. The nodding scan is also used with height-finding radars. 
The Palmer, spiral, and raster scans are employed in fire-control tracking radars to 
assist in the acquisition of the target when the search sector is of limited extent. 



192 



Introduction to Radar Systems 



[Sec. 5.9 



5.9. Examples of Tracking Radars 

The major characteristics of three tracking radars will be presented for the purpose of 
illustration. The three trackers are (1) the SCR-584, (2) the MIT Lincoln Laboratory 
Millstone Hill radar, and (3) the AN/FPS-16. 

The SCR-584 38 was the first successful operational tracking radar at microwave 
frequencies (Fig. 5.19). It was developed by the MIT Radiation Laboratory and 
became available in operational quantities during the latter half of World War 1 1. Its 
function was to provide the fire-control information necessary for operating a battery 
of four 90-mm antiaircraft guns. The SCR-584 was the first to use the conical-scan 




Fig. 5.19. SCR-584 tracking radar. (Courtesy McGraw-Hill Book Company, Inc.) 

tracking technique. Its basic principle of operation was not too unlike that of modern 
conical-scan trackers. The radar was also designed to operate in a search mode to 
provide its own acquisition information. When searching, the beam scanned a helical 
pattern with 360° azimuth coverage and a reasonable amount of elevation coverage. 
The target information obtained during the search phase was displayed on a PPL 
When a suitable target was found, the search pattern was stopped and the antenna was 
positioned to acquire the target. The target-tracking data supplied by the radar were 
processed in an analog computer which smoothed the data, predicted the target's future 
position, and computed the lead angle for the guns. The output information actuated 
a servo system that positioned the guns according to orders from the computer. 

The SCR-584 was designed originally to operate at 5 band. An A"-band version was 
also produced. A list of the parameters of the 5-band version is presented in Table 5.1. 

The SCR-584 considerably improved the capabilities of antiaircraft artillery when it 
was introduced during World War II. Although it was not the first fire-control radar 
used by the military for aiming antiaircraft guns, its accuracy and especially its angular 
resolution were superior to the VH F and U HF radars then in use. Its introduction was 
particularly important in World War II since the Germans had devised electronic 
countermeasures against the existing SCR-268 tracking radars but did not have the 



Sec. 5.9] 



Tracking Radar 193 



means for jamming the microwave frequencies. After the war, ready availability of 
the SCR-584 made it popular as an instrumentation radar for drone or missile tracking 
and for research and development programs requiring a flexible radar. A modified 
version of the SCR-584 is the AN/MPQ-12, also listed in Table 5.1. It employs a 
larger antenna and has more range capability. The Army M-33 fire-control radar that 
replaced the SCR-584 can also be considered of comparable performance, although of 
different design. 

A large conical scanning UHF radar is the MIT Lincoln Laboratory radar (Fig. 5.20) 
located on Millstone Hill in Westford, Mass. 40 This radar is similar in principle to the 
SCR-584 tracker, but in detail it is quite different because its application is different. 

Table 5.1. Comparison of Trackers 



Characteristic 



Type of tracking 

Antenna size, ft 

Frequency 

Beamwidth, deg 

Antenna gain, db 

Power: 

Peak 

Average 

Pulse width 

Prf, cps 

Receiver noise figure, db 
Receiver bandwidth, Mc 
Accuracy : 

Range 

Angle 

Range on 1-m 2 target, 
nautical miles: 

For detection 

For accurate track . . . 



SCR-584 



Conical scan 

6 

Sband 

4 

33 

250 kw 
340 watts 
0.8 /isec 
1,707 
15 
1.7 

20 yd 
2 mils 



30 
15 



AN/MPQ-12 



Conical scan 

10 

5 band 

2.4 

37 

250 kw 

0.25 ,usec 
364-1,707 
12 



10 yd 
lmil 



70 
35 



AN/FPS-16 



Monopulse 

12 

Cband 

1.2 

44.5 

1 Mw 

lkw 

0.25,0.5, l.OjUsec 

160-1,707 

11 

8.0 or 1.6 

5 yd 
0.1 mil 



180 
120 



Millstone Hill 



Conical scan 

84 

UHF (440 Mc) 

2.1 

37.5 

2.5 Mw 
150 kw 
2 msec 
30 
2 



8 km 
0.2° 



2,000 



The Millstone Hill radar was designed to track objects such as satellites, missiles, the 
moon, and similar objects beyond or within the earth's atmosphere. Its parabolic 
antenna is 84 ft in diameter and is supported 90 ft above the ground. Heavy-duty 
drive motors permit the antenna to track in azimuth and elevation at the rate of 4°/sec. 
A turnstile junction located just behind the circular feed horn allows the transmitted 
signal to have any polarization, from linear to circular to elliptical. The turnstile also 
permits receiving on two orthogonal polarizations. (This feature is necessary when 
UHF energy is propagated through the ionosphere because of Faraday rotation; see 
Sec. 14.2.) The size of waveguide used at this frequency is 10i by 21 in. 

The transmitter consists of two high-power klystron amplifiers operating in parallel, 
similar to the X626 described in Sec. 6.3. Two identical receivers process the returned 
echo signal, one for each orthogonal polarization. The signal in each receiver is 
divided into two channels. One channel contains a matched filter bank from which 
digital-range and doppler information is extracted. The other channel contains a 
coherent (phase) detector of wide dynamic range for extracting the phase and amplitude 
characteristics of the returned signal. The radar output data are in digital form for 
processing in the CG-24 transistorized digital computer. 

An example of a monopulse tracking radar is the AN/FPS-16 (Fig. 5.21), the charac- 
teristics of which are tabulated in Table 5.1. 15 - 25 The FPS-16 is an instrumentation 
radar, designed especially for precision tracking of guided missiles. The trailer- 
mounted mobile version is the AN/MPS-25. Angular accuracy of the FPS-16 after 



194 Introduction to Radar Systems 



[Sec. 5.9 




Fig. 5.20. MIT Lincoln Laboratory Millstone Hill radar. (Courtesy MIT Lincoln Laboratory.) 



„.j- "i" 



A 




■ 



■f ■ o . :«*i..* I&f&ter WrSfceaTWAfc.. 



Fig. 5.21. AN/FPS-16 tracking radar. (Courtesy Radio Corporation of America.) 



Sec. 5.10] Tracking Radar 195 

correction for propagation effects is 0. 1 mil. (A mil is one-thousandth of a radian, or 
17.4 mils = 1°.) This is an order of magnitude better than that of the SCR-584. For 
the achievement of an accuracy as good as 0.1 mil, careful designing was required. 
The four-horn monopulse feed is supported in front of the reflector by four invar rods. 
The antenna is 12 ft in diameter, and the entire azimuth turntable rotates on a ball- 
bearing race 60 in. in diameter. The mechanical resonance on the entire structure is 
above 15 cps, permitting a closed-loop servo response of 5 cps. The radar is painted 
with a white, heat-reflecting paint to minimize mechanical errors caused by temperature 
gradients induced by solar radiation. Tracking in azimuth can be accomplished at a 
rate of 40°/sec. The elevation tracking rate is 30°/sec. The AN/FPQ-6, an improved 
version of the AN/FPS-16, has a 29-ft-diameter Cassegrain antenna and radiates 3 Mw 
peak power at C band. 45 

5.10. Comparison of Trackers 

Of the four continuous-tracking-radar techniques that have been discussed (sequen- 
tial lobing, conical scan, amplitude-comparison monopulse, and phase-comparison 
monopulse), conical-scan and amplitude-comparison monopulse probably have seen 
more application than the other two. The phase-comparison monopulse has not 
proved too popular. It does not make efficient use of the available antenna aperture, 
and the sidelobe level might sometimes be higher than if a single antenna were used. 
Sequential lobing is similar to conical-scan tracking. Conical-scan tracking seems to 
be preferred in most applications because it is usually more practical to implement than 
sequential lobing. Therefore, in this section, only the conical-scan radar and the 
amplitude-comparison monopulse will be compared. (The latter will be referred to 
simply as monopulse.) The comparison of the monopulse and conical-scan trackers 
is made on the bases of detectability, tracking accuracy, and complexity. 

There is little significant difference between the detection capability of conical-scan 
and monopulse trackers when the major parameters of the radar (those which appear 
in the radar equation) are the same. Both radar techniques result in some slight loss of 
antenna gain over a nontracking antenna of the same size because of the offset antenna 
beams. 

The tracking accuracy of the conical-scan radar is degraded if the target cross section 
fluctuates in amplitude at frequencies at or near the conical-scan frequency. Amplitude 
fluctuations have essentially no effect on monopulse radar. However, wandering of 
the apparent radar center (glint) increases the tracking error of both types of radars. 
For equal signal-to-noise ratios and antenna beamwidths, the tracking accuracy of the 
two systems should be comparable in the absence of amplitude fluctuations. Generally, 
amplitude fluctuations are always present with complex targets so that the monopulse 
radar is preferred when tracking accuracy is important. 

The monopulse radar is the more complex of the two. Three separate receivers are 
necessary to derive the error signal in two orthogonal angular coordinates; only one 
receiver is needed in the conical-scan radar. Since the monopulse radar compares the 
amplitudes of the signals received in two or more channels, it is important that the gain 
of and phase shift through these channels be identical. Any differences in the gain or 
the phase might be interpreted as an erroneous angular error. (A change in relative 
phase can result in an amplitude difference.) It is usually difficult to maintain amplitude 
or phase stability in the RF portions of the receiver where the path length is many 
wavelengths long. For this reason, the RF circuitry in the monopulse radar is usually 
placed as close to the antenna feed as possible. Many monopulse trackers employ lens 
antennas (Sec. 7.6) or Cassegrain reflectors (Sec. 7.5) which permit the RF circuitry to 
be placed directly at the feed without blocking the aperture. 

With the monopulse tracker it is possible, in principle, to obtain a measure of the 



196 Introduction to Radar Systems 

angular error in two coordinates on the basis of a single pulse ; a minimum of four 
pulses are necessary with the conical-scan radar. Thus the monopulse tracker is 
theoretically capable of obtaining an angle measurement in microseconds as compared 
with milliseconds for the conical-scan radar. If the signal-to-noise ratio per pulse were 
sufficiently large, the monopulse tracker would be capable of responding to faster 
angular rates than the conical-scan tracker and would be limited only by the response of 
the mechanical structure of the radar antenna and the servos. If the two radars are to 
be evaluated on the same basis, however, the total echo energy ought to be the same. 
Therefore they should both integrate the same number of pulses. In essence, the 
monopulse radar first makes its measurement and then integrates a number of pulses to 
obtain the required output signal-to-noise ratio; the conical-scan radar does the 
opposite. It integrates a number of pulses first and then extracts the angular error. 
The faster response of the monopulse tracker may be obtained only when the signal-to- 
noise ratio per pulse is of sufficient magnitude (20 to 30 db) to allow a good measurement 
to be made on a single pulse without the necessity for integration. 

Because the accuracy of monopulse is not degraded by amplitude fluctuations, it is 
less susceptible to electronic countermeasures than is conical scan. 

In summary, it may be said that the performances of the conical-scan radar and the 
monopulse radar are quite comparable except when the amplitude of the target cross 
section fluctuates at a rate comparable with the conical-scan frequency. When target 
amplitude fluctuations are troublesome, they may be eliminated with the slightly more 
complex monopulse radar. 

REFERENCES 

1. James, H. M., N. B. Nichols, and R. S. Phillips: "Theory of Servomechanisms," MIT Radiation 
Laboratory Series, vol. 25, McGraw-Hill Book Company, Inc., New York, 1947. 

2. Schafer, C. R.: Phase-selective Detectors, Electronics, vol. 27, no. 2, pp. 188-190, February. 
1954. rr } 

3. Greenwood, I. A., Jr., J. V. Holdam, Jr., and D. Macrae, Jr. (eds.): "Electronic Instruments," 
MIT Radiation Laboratory Series, vol. 21, pp. 383-386, McGraw-Hill Book Company, Inc 
New York, 1948. v } 

4. Palma-Vittorelli, M. B., M. U. Palma, and D. Palumbo: The Behavior of Phase-sensitive Detec- 
tors, Nuovo cimento, vol. 6, pp. 1211-1220, Nov. 1, 1957. 

5. Krishnan, S.: Diode Phase Detectors, Electronic and Radio Engr., vol. 36, pp. 45-50, February, 

6. Lawson, J. L., and G. E. Uhlenbeck (eds.): "Threshold Signals," MIT Radiation Laboratory 
Series, vol. 24, McGraw-Hill Book Company, Inc., New York, 1950. 

7. Oliver, B. M.: Automatic Volume Control as a Feedback Problem, Proc. IRE, vol. 36 pp 
466-473, April, 1948. yv ' 

8. Field, J. C. G.: The Design of Automatic-gain-control Systems for Auto-tracking Radar 
Receivers, Proc. IEE, pt. C, vol. 105, pp. 93-108, March, 1958. 

9. Locke, A. S.: "Guidance," pp. 402^108, D. Van Nostrand Company, Inc., Princeton, N.J., 

10. Damonte, J. B., and D. J. Stoddard: An Analysis of Conical Scan Antennas for Tracking, IRE 
Natl. Conv. Record, vol. 4, pt. 1, pp. 39-47, 1956. 

11. Whittaker, E. T., and G. N. Watson: "Modern Analysis," 4th ed., p. 357, ex. 3, and p. 372 
Cambridge University Press, New York, 1950. 

12. Kleene, S. C: Analysis of Lengthening of Modulated Repetitive Pulses, Proc. IRE, vol 35 
pp. 1049-1053, October, 1947. 

13. Page, R. M.: Monopulse Radar, IRE Natl. Conv. Record, vol. 3, pt. 8, pp. 132-134, 1955. 

14. Dunn, J. H., and D. D. Howard: Precision Tracking with Monopulse Radar, Electronics, vol. 33 
no. 17, pp. 51-56, Apr. 22, 1960. 

15. Barton, D. K., and S. M. Sherman: Pulse Radar for Trajectory Instrumentation, paper presented 
at Sixth National Flight Test Instrumentation Symposium, Instrument Society of America San 
Diego, Calif., May 3, 1960. 

16. Cohen, W., and C. M. Steinmetz: Amplitude and Phase-sensing Monopulse System Parameters, 
pts. I and II, Microwave J., vol. 2, pp. 27-33, October, 1959, and pp. 33-38, November, 1959- 
also discussion by F. J. Gardiner, vol. 3, pp. 18, 20, January, 1960. 



Tracking Radar 197 

17. Rhodes, D. R.: "Introduction to Monopulse," McGraw-Hill Book Company, Inc., New York, 

1959 

18. Tyrrell, W. A.: Hybrid Circuits for Microwaves, Proc. IRE, vol. 35, pp. 1294-1306, November, 

1947 

19. Downey, E. J., R. H. Hardin, and J. Munishian: A Time Duplexed Monopulse Receiver, Conf. 
Proc. on Military Electronics Conv. (IRE), 1958, p. 405. 

20 Shelton, J. P., Jr. : Improved Feed Design for Amplitude Monopulse Radar Antennas, IRE Natl. 
' Conv. Record, vol. 7, pt. 1, pp. 93-102, 1959. 

21 Price, O. R., and R. F. Hyneman: Distribution Functions for Monopulse Antenna Difference 
' Patterns, IRE Trans., vol. AP-8, pp. 567-576, November, 1960. 

22 Blewett J P , S. Hansen, R. Troell, and G. Kirkpatrick: The Multilobe Tracking System, report 
' from the General Electric Co. Research Laboratory, Schenectady, N.Y., Jan. 5, I 944 - 

23. Sommer, H. W.: An Improved Simultaneous Phase Comparison Guidance Radar, IRE Trans., 
' vol. ANE-3, pp. 67-70, June, 1956. . 

24 Barton D K • Application of Precision Tracking Radar to Location, Control and Data Trans- 
' mission for an Unmanned Observation Platform, Proc. Natl. Conf. on Aeronaut. Electronics, 

25 Barton P D. K.: Accuracy of a Monopulse Radar, Proc. Third Natl. Military Electronics Conv. 
' (IRE), June 30, 1959, pp. 179-186. ,„..„• ™ • • D a 

26 Dunn, J. H., D. D. Howard, and A. M. King: Phenomena of Scintillation Noise in Radar 
' Tracking Systems, Proc. IRE, vol. 47, pp. 855-863, May, 1959. 

27 Locke, A. S. : "Guidance," pp. 440-442, D. Van Nostrand Company, Inc., Princeton, N.J., 1955. 

28 Delano, R. H. : A Theory of Target Glint or Angular Scintillation in Radar Tracking, Proc. IRE, 
' vol. 41,' pp. 1778-1784, December, 1953. 

29 Freeman, J. J.: "Principles of Noise," chap. 10, John Wiley & Sons, Inc., New York 1958 

30. Bendat, J. S.: "Principles and Applications of Random Noise Theory," sec. 5.9-1, John Wiley 
& Sons', Inc., New York, 1958. . 

3 1 Howard D D. : Radar Target Angular Scintillation in Tracking and Guidance Systems Based on 
Echo Signal Phase Front Distortion, Proc. Natl. Electronics Conf. (Chicago), vol. 15, pp. 840-849, 

1959 

32 Muchmore, R. B.: Aircraft Scintillation Spectra, IRE Trans., vol. AP-8, pp. 201-212, March, 
' 1960; also discussions by L. Peters, Jr., F. C. Weimer, and R. B. Muchmore, vol AP-9, pp. 

110-113, January, 1961, and by R. H. Delano, K. M. Siegel, L. Peters, Jr., and F. C. Weimer, 
vol. AP-9, pp. 227-229, March, 1961. 

33 Dunn J H and D D. Howard: The Effects of Automatic Gain Control Performance on the 
' Tracking Accuracy of Monopulse Radar Systems, Proc. IRE, vol. 47, pp. 430^135, March, 1959. 

34. Delano, R. H., and I. Pfeffer: The Effect of AGC on Radar Tracking Noise, Proc. IRE, vol. 44, 
pp. 801-810, June, 1956. . 

35. Brockner, C. E.: Angular Jitter in Conventional Conical Scanning Automatic-tracking Radar 
' Systems, Proc. IRE, vol. 39, pp. 51-55, January, 1951. „„,,.„. D . _ _ , 

36. Swerling, P.: Some Factors Affecting the Performance of a Tracking Radar, Rand Corp. Rept. 
RM-989-1, Santa Monica, Calif., Sept. 27, 1954. 

37 Locke A S : "Guidance," pp. 408-413, D. Van Nostrand Company, Inc., Princeton, N.J., 1955. 
38' The SCR-584 Radar, Electronics, pt. 1, vol. 18, pp. 104-109, November, 1945; pt. 2, vol. 18, 
pp. 104-109, December, 1945; pt. 3, vol. 19, pp. 110-117, February, 1946. 

39 Cady W M., M. B. Karelitz, and L. A. Turner (eds.): "Radar Scanners and Radomes, MIT 
' Radiation Laboratory Series, vol. 26, p. 66, McGraw-Hill Book Company, Inc., New York, 1948. 

40 Petteneill G H., and L. G. Kraft, Jr.: Earth Satellite Observations Made with the Millstone Hill 
Radar, paper in "Avionics Research," Advisory Group for Aeronautical Research and Develop- 
ment (AGARD), NATO, Pergamon Press, New York, 1960. 

41. "IRE Dictionary of Electronics Terms and Symbols," Institute of Radio Engineers, New York, 

42 Eisengrein R H.: "Design of Fire-control Systems," Part II, Measurement and Analysis of 
' Noise in a Fire-Control System, MIT Servomechanisms Laboratory, Cambridge, Mass., under 

Contract W-33-038ac-13969, 1950. (Not generally available.) Communicated to the author 
by J. E. Ward. , „ „ , , .. , 

43 Gardner R E : Doppler Spectral Characteristics of Aircraft Radar Targets at 5-band, Naval 
' Research Lab. Rept. 5656, Aug. 3, 1961 (ASTIA No. AD 263478). 

44. Stryker, E. M.: The Use of a Tuned Discriminator in Tracking a Doppler Navigation Radar 
Spectrum, Proc. Natl. Conf. on Aeronaut. Electronics, 1959, pp. 228-231. 

45. Mason, J. F.: New Pulse Trackers Readied for Space Ranges, Electronics, vol. 34, no. 50, pp. 
26-28, Dec. 15, 1961. 



6 



RADAR TRANSMITTERS 



6.1. Introduction 

Generation of adequate RF power is an important part of any radar system. The 
radar equation of Chap. 2 shows that the transmitter power varies as the fourth root of 
the range if all other factors are constant. To double the range, the power has to be 
increased 16-fold. Buying range at the expense of power is costly; it is therefore 
important that the best transmitter be selected for any particular application. Not 
only does a transmitter represent a large part of the initial cost of a radar system, but 
unlike many other parts of the radar, it requires a continual operating cost because of 
the need for prime power or fuel. 

There are two basic transmitter configurations used in radar. One is the self-excited 
oscillator, exemplified by the magnetron. The other utilizes a low-power, stable 
oscillator, which is in turn amplified to the required power level by one or more power- 
amplifier tubes. An example is the klystron amplifier fed by a crystal-controlled, 
frequency-multiplier chain, sometimes referred to as MOPA, an abbreviation for 
master-oscillator power amplifier. Both of these transmitter configurations were 
encountered in the discussion of the MTI radar in Sec. 4.1. The choice between the 
two is governed mainly by the radar application. Transmitters that utilize self- 
excited power oscillators are usually smaller than transmitters with master-oscillator 
power amplifiers (MOPA). The latter are more stable than self-excited oscillators 
and are usually capable of greater average power. Self-excited power oscillators 
therefore are likely to be found in applications where small size and portability are more 
important than the stability and high power of the MOPA. 

The earliest radar transmitters operated below the microwave region in the UHF and 
VHF bands. Conventional triodes and tetrodes were used since no other power tubes 
were available. The invention of the cavity magnetron by Randall and Boot in the late 
thirties made possible the development of microwave radar in time for World War II. 
The magnetron oscillator has seen wide application in radar. In the years following 
World War II, the potentialities of the klystron amplifier as a radar transmitter were 
realized, and it began to be applied early in the 1950s in radars where large power and 
good stability were required. 

Also, in the years following the war, further development of grid-controlled tubes for 
high-power UHF applications took place, primarily because of the needs of commercial 
television. High-power triodes and tetrodes thus became available for radar applica- 
tion at frequencies up to approximately 1,000 Mc. These tubes were capable of 
delivering, from a single "bottle," average power outputs greater than those obtained 
from any other tube type operating in this frequency range. 

The high-power traveling-wave-tube amplifier may also be used for radar application, 
especially where large transmitter bandwidth is required. 

Another high-power amplifier tube found in radar is the Amplitron. It is based 
upon the principle of crossed electric and magnetic fields just as is the magnetron 
oscillator. The Amplitron is characterized by high power, high efficiency, and broad 
bandwidth. The oscillator version is called the Stabilitron. 

In this chapter various tube types used for high-power radar transmitter application 
will be discussed. Those considered are the magnetron oscillator, klystron amplifier, 

198 



Sec. 6.2] Radar Transmitters 199 

traveling-wave tube, Amplitron, Stabilitron, and the grid-controlled tube, listed not 
necessarily in the order of their importance. The basic operating principles of these 
tubes will be only briefly mentioned. Emphasis will be on the properties of importance 
in radar applications. There are many texts available on microwave tubes, as well as a 
large published literature, where the interested reader can find the details concerning 
the theory of each type of tube. 

Also discussed is the modulator, which turns the transmitter on and off to form the 
transmitted waveform. 

6.2. The Magnetron Oscillator 

Historical Development. 1 ' 2, The name magnetron has been applied in the past to 
several different types of electron devices. All of these are diodes, usually with 
cylindrical geometry, and with a magnetic field parallel to the axis (perpendicular to the 
electric field). The original magnetron device was a diode switch invented in 1921 by 
A. W. Hull. The application of the magnetic field deflected the electrons from their 
journey to the plate and cut off the conduction of the tube. Hull also observed oscil- 
lations from his magnetron at a frequency of 30 kc. A power of 8 kw was obtained 
with an efficiency of 69 per cent. The oscillations were due to the cyclotron resonance 
frequency that is characteristic of electrons in crossed electric and magnetic fields. 
Cyclotron oscillations were observed at microwave frequencies by Zacek, in Prague, 
at a wavelength of 29 cm as early as 1924. Yagi, in Japan, also obtained microwave 
cyclotron oscillations at about the same time. Although extremely high frequencies 
have been generated with cyclotron magnetrons, they have not been too widely used 
since they suffer from low power, erratic behavior, and low efficiencies at microwave 
frequencies (1 per cent for the cylindrical diode magnetron, about 10 per cent for the 
split-anode magnetron at moderately long wavelengths). 

With a magnetic field large compared with that used for the cyclotron magnetron, a 
more efficient and reliable form of magnetron is obtained based on negative-resistance 
oscillations. This is sometimes called Habann-type oscillations, after Eric Habann, 
who theoretically predicted and experimentally demonstrated their existence. The 
frequency of oscillation is determined by the resonant circuit. The magnetic field is 
not as critical with the negative-resistance magnetron as it is with the cyclotron magne- 
tron. 

K. Postumus, in 1935, reported a third form of magnetron known as the traveling- 
wave magnetron (not to be confused with the traveling-wave tube invented later). The 
modern radar magnetron is based upon this principle. The magnetron of Postumus 
consisted of an anode split into four segments. Oscillations were due to an interaction 
between the electrons and the tangential component of a traveling- wave RF field whose 
velocity was substantially equal to the average velocity of the electrons. Various 
investigators reported microwave oscillations with this magnetron in the late 1930s, 
but further development for high-power applications had to await a better under- 
standing of the principles of microwave circuits, especially the role played by the cavity 
resonator. Fortunately, the understanding of microwave circuitry was also being 
actively pursued at about this same time, but with application to the klystron amplifier 
rather than the magnetron. 

The first successful magnetron suitable for radar application was invented by 
Randall and Boot at the University of Birmingham in 1939. 3 They were not too 
familiar with the earlier investigations of magnetrons, so they were not influenced by 
the pessimistic outlook this work seemed to dictate. They were familiar, however, 
with the early experimental work with klystron amplifiers, especially the application of 
cavity resonators. Randall and Boot applied the cavity resonators to the magnetron 
structure and produced a magnetron at 10 cm wavelength capable of better than 100 kw 



200 



Introduction to Radar Systems 



[Sec. 6.2 



of pulse power, a power considerably greater than had previously been achieved at these 
frequencies. The British disclosed the principle of the cavity-resonator magnetron to 
the United States in 1940 during an exchange of technical information just prior to our 
entry into World War II. The magnetron, more than any other single device, formed 
the basis for the development of microwave radar in this country. 

Description of Operation. 1 The magnetron is a crossed-field device ; that is, the 
electric fields (both RF and d-c) are perpendicular to a static magnetic field. The 
development of the magnetron has probably relied less on theoretical results and more 
on the empirical approach to design than other tube types, since cross-field devices, 
including the magnetron and the Amplitron, are not readily susceptible to mathemati- 
cal analysis. 




Fig. 6.1. Cross-sectional sketch of typical cavity magnetron illustrating component parts. 

The basic structure of one form of magnetron is shown in Fig. 6. 1 . The anode (1) is a 
large block of copper into which are cut holes (2) and slots (3). The holes and slots 
function as the resonant circuits and serve the same purpose as the lumped-constant LC 
resonant circuits used at lower frequencies. The holes correspond, in rough fashion, 
to the inductance, while the slots correspond to the capacity. The resonant circuits 
all lie within the vacuum envelope in the magnetron. Other forms of resonators which 
might be used are the slots shown in Fig. 6.2a or the vanes in 6.2b. The shape of the 
cavities determines the impedance (which is equal to L/C). The slot configuration has 
a lower impedance than the vane configuration. In the desired mode of operation 
(the 77 mode) the individual C's and Us are connected in parallel. The effective 
capacitance for the whole magnetron oscillator is NC, and the effective inductance is 
LjN, where N is the number of resonators. Since the angular frequency is equal to 
(LC)~-, the frequency of the magnetron is essentially that of an individual resonator. 

Another type of resonator structure found in some magnetrons is the interdigital 
anode. 4 This structure has been widely used in voltage-tuned magnetrons. The 
resonator of the interdigital magnetron is a short cylindrical cavity. The anode 
segments extend as fingers from the two flat sides of the cavity. Alternate segments are 
connected together at one end of the cavity, and the remaining segments are connected 
together at the opposite end. This type of anode has also been called a squirrel cage, 
or a donutron. 



Sec. 6.2] 



Radar Transmitters 201 




(a) 



The magnetron cathode (4, Fig. 6. 1) is usually a fat cylinder of oxide-coated material. 
The advantage of the oxide cathode is that higher emission currents can be obtained 
under pulse conditions than with other emitting materials. For example, 5 under d-c 
conditions an oxide cathode is capable of an emission-current density of the order 
of 0.2 amp/cm 2 , but under pulse conditions the emission current can be as great as 
1 00 amp/cm 2 . The cathode must be rugged to withstand the heating and disintegration 
caused by the back bombardment of electrons. BacK bombardment increases the 
cathode temperature during operation and causes secondary electrons to be emitted. 
For this reason the heater power may be reduced or even turned off once oscillations 
have started. The relatively fat cylindrical cathode can dissipate more heat than a thin 
cathode. A fat cathode is also required for theoretical 
reasons. The optimum ratio of the cathode diameter to 
anode diameter equals, or slightly exceeds, (N — 4)/(iV+ 4), 
where N is the number of resonators. This ratio is equal 
to one-half for a 12-cavity magnetron. 

Most magnetrons in the past used a cathode consisting 
of a matrix of nickel powder sintered on the nickel-alloy 
base metal providing a rough, porous surface for the im- 
pregnation of a tenacious layer of the oxide-emitting sur- 
face. 6 Another cathode that has been used is the dispenser 
cathode, 7 in which the oxide is impregnated in a tungsten 
cylinder (called the impregnated type) or else the oxide 
material is made to diffuse through tungsten (called Z,-type 
cathode). Since a refractory metal serves as the cathode 
base, it can withstand high temperatures and severe arcing 
conditions better than can the matrix oxide cathode. 

In the interaction space (5, Fig. 6.1) the electrons inter- 
act with the d-c electric field and the magnetic field in such 
a manner that the electrons give up their energy to the RF 
field. The presence of the crossed electric and magnetic 
fields causes the electrons to be completely bunched almost 
as soon as they are emitted from the cathode. After be- 
coming bunched, the electrons move along in a traveling- 
wave field. This traveling-wave field moves at almost the 
same speed as the electrons, causing RF power to be de- 
livered to the wave. The RF power is extracted by placing 
a coupling loop in one of the cavities as shown (6, Fig. 6.1) 

or else by coupling one cavity directly to a waveguide. Not shown in Fig. 6. 1 are end- 
shield disks located at each end of the cathode for the purpose of confining the 
electrons to the interaction space. If electrons are lost from the ends of the cathode, 
their power is not delivered to the RF field and the efficiency of the tube will decrease. 
In addition, the frequency stability will be poorer. 

The straps (7, Fig. 6.1) are metal rings connected to alternate segments of the anode 
block. They improve the stability and efficiency of the tube. 

Figure 6.3 is an exploded view of the QIC 358 tunable L-band magnetron showing the 
component parts. An assembled QK 358 is shown in Fig. 6.4. 

Stability}'* The preferred mode of magnetron operation corresponds to an RF 
field configuration in which the RF phase alternates 180° between adjacent cavities. 
This is called the n mode. Its frequency is approximately the resonant frequency of 
one of the cavity resonators. The presence of more than one cavity in the magnetron 
results in JV/2 possible modes of operation, where N is the total number of cavities. 
The various modes are a result of mutual coupling between cavities. Each of the N/2 




Fig. 6.2. Examples of cavity- 
magnetron resonators, (a) 
Slot type; (b) vane type. 



202 



Introduction to Radar Systems 



[Sec. 6.2 

modes corresponds to a different RF field configuration made up of a standing wave of 
charge. All the modes except the n mode are degenerate; that is, they can oscillate at 
two different frequencies corresponding to a rotation of the standing-wave pattern, 
where the positions of the nodes and antinodes are interchanged. Thus there are N — 1 
possible frequencies in which the magnetron can oscillate. The presence of more than 



TUNING GEAR 
ASSEMBLY- 



MAGNET 

(ONE OF 4 SECTIONS), 



EXHAUST SEAL 
TUBULATION 



GETTER TERMINAL 
SETTER MATERIAL 




TUNER POLE 



BELLOWS HOUSING 
AIR DUCT HOUSING 



AIR DUCT COUPLING 
FLANGE 



output transformer 

JBP\xeramic 
^,^" r.f. output 

»*■ 1 WINDOW 



CATHODE- 
CATHODE END SHIELDS- 




HEATER TERMINAL 
CUP ASSEMBLY 



Fig. 6.3. Exploded view of a Raytheon RK6517/QK358 tunable L-band magnetron, capable of 
1 Mw of peak power at a duty factor of 0.001 3. (Courtesy Raytheon Company.) 

one possible mode of operation means that the magnetron can oscillate at any one of 
these frequencies and can do so in an unpredictable manner. This is the essence of the 
stability problem. A different mode means a different frequency and a different field 
configuration. An output circuit designed for one particular mode configuration may 
produce a weak or a zero output when the magnetron operates in a different mode. 
Therefore it is important that a magnetron be designed with but one mode dominant. 



Sec. 6.2] Radar Transmitters 203 

The it mode is usually preferred because it is not degenerate and can be more readily 
separated from the others. 

The early magnetron invented by Randall and Boot suffered from frequency in- 
stability and inefficiency as a result of moding troubles. About a year after the 
invention of the cavity magnetron, Sayre, at the University of Birmingham, found that 
the stability and efficiency of the tube could be considerably improved by coupling 
together every other segment with a circular ring called a strap, as was shown in Fig. 
6.1. The cross section of the straps may be either circular or rectangular. The straps 
connect all those segments which have the same potential in the n mode. Various 
forms of strapping are discussed by Walker in Ref. 1 , Chap. 4. 




Fig. 6.4. Photograph of RK 6517/QK 358 Z-band magnetron. (Courtesy Raytheon Company.) 

In a particular eight-resonator, unstrapped magnetron operating at 1 cm wavelength 
(3,000 Mc), the frequency of the -rr mode was separated by less than 2 per cent from its 
next nearest degenerate mode. 1 A single ring strap increased the separation to greater 
than 10 per cent. Even greater mode separation is possible if larger or more straps are 
used. In a strapped symmetrical magnetron, the lowest frequency is that correspond- 
ing to the 77 mode. Strapping not only improves the stability of operation, but it also 
increases the efficiency, since higher powers can be obtained without fear of mode 
changing. For example, the early unstrapped British magnetrons were unstable and 
had efficiencies of 30 to 35 per cent. Strapping improved the stability and increased 
the efficiency to 50 per cent. 

Strapping is not the only method of obtaining mode stability. Four- or six-segment 
anode blocks can be made to function in the -n mode without straps because there are 
few modes to separate. Another technique is the interdigital anode block. In the 
interdigital magnetron there are no individual resonators as such, but there is a closed 
transmission line with segments (digits) attached alternately to opposite conductors of 
the line. The modes are readily separated in this construction, but the tube is limited 
to low power. 



204 Introduction to Radar Systems 



[Sec. 6.2 




Fig. 6.5. Rising-sun magnetron resonator. 



Another method of separating the modes in the magnetron is with the rising-sun anode 
configuration 9 (Fig. 6.5). This structure separates the modes without the need for 
straps. It is of particular advantage at the very high radar frequencies (X band or 
above), where it is difficult to manufacture strapped magnetrons because of their small 
size. Also, the straps have relatively high copper losses at these frequencies. The 
rising-sun structure may also be used for high-power applications at the longer wave- 
lengths. 

The rising-sun anode block is characterized by alternately large and small resonators. 
In general, there are more cavities in the rising-sun magnetron than in the conventional 

magnetron. The rising-sun anode may be 
considered as two resonant systems, one com- 
prising the small cavities, and the other, the 
large cavities. Each of these systems by itself 
would have the mode spectrum of an un- 
strapped magnetron block with N/2 resona- 
tors. Weak coupling exists between the 
various modes of the two sets of resonators 
except for the 77 mode. The coupling between 
the 7T modes of the two systems is strong, 
and they combine to produce the operating 
mode. In the rising-sun system the n mode 
lies between the groups of other undesired 
modes at longer and at shorter wavelengths, 
whereas in the strapped magnetron the tt 
mode corresponds to the longest wavelength. 
The rising-sun magnetron has been used 10 to 
generate RF power at wavelengths as short as 3 mm. It is quite suitable for high 
power because of the relatively large cavity resonators, large cathode and anode 
diameters, and long anodes. 

Performance Chart andRieke Diagram. 1 ' 11 Four parameters determine the operation 
of the magnetron. These are (1) the magnetic field, (2) the anode current,! (3) load 
conductance, and (4) load susceptance. The first two parameters are related to the 
input side of the tube, while the last two are related to the output side. In many 
magnetrons the magnetic field is fixed by the tube designer and may not be a variable the 
radar designer has under his control. The observed quantities are usually the output 
power, the wavelength, and the anode voltage. The problem of presenting the varia- 
tion of the three quantities — power, wavelength, voltage — as a function of the four 
parameters mentioned above is greatly simplified since the input and output parameters 
operate nearly independently of each other. Thus it is possible to study the effect of 
the magnetic field and the anode current at some value of load susceptance and con- 
ductance chosen for convenience. The results will not be greatly dependent upon the 
particular values of susceptance and conductance chosen. Similarly, the variation of 
the observed quantities can be studied as a function of the load presented to the magne- 
tron, with the input parameters — magnetic field and current — likewise chosen for 
convenience. The plot of the observed magnetron quantities as a function of the input 
circuit parameters, for some fixed load, is called the performance chart. The plot of the 
observed quantities as a function of the load conductance and susceptance, for a fixed 
magnetic field and anode current, is called a Rieke diagram, or a load diagram. 

An example of a performance chart is shown in Fig. 6.6. This is representative of 

t The anode voltage might be substituted for the anode current, except that a magnetron behaves 
more like a current generator than a voltage generator. The current determines the voltage, and not 
vice versa. 



Radar Transmitters 



205 



Sec. 6.2] 

the Raytheon 4J36-4J41 pulse-type S-band magnetrons. The abscissa is the peak 
anode current, and the ordinate is the peak anode voltage. The data plotted in the 
performance chart are for a fixed load, usually a matched load. There are four 
families of curves shown on this chart. The curves of constant magnetic field (solid 
lines) approximate straight lines, of relatively small positive slope, except for small 
values of current. If the magnetron were supplied with a fixed magnetic field chosen 
by the tube designer, only one curve of constant magnetic field would apply and the 
performance chart would be considerably simplified. The contours of constant (peak) 

30 




30 40 

Peak current, amp 

— — — Magnetic field 

— - — Peak power output 

Magnetron efficiency 

Deviation in frequency from OMc 



{Courtesy Raytheon 



Fig. 6.6. Performance chart for the type 4J36-4J41 pulsed magnetron oscillator. 
Company.) 

power output (heavy dashed lines) suggest the form of hyperbolas. For a constant 
output power the performance chart shows the compromises which can be made 
between the voltage, current, efficiency, and magnetic field. This particular perform- 
ance chart indicates that the magnetron will produce a power output of 500 kw with a 
peak anode voltage = 26 kv, peak anode current = 38 amp, and magnetic field = 2,500 
gauss. The magnetron efficiency is 50 per cent under these conditions. If the current 
is kept the same but the magnetic field reduced to slightly more than 1,500 gauss, the 
peak anode voltage is 14.5 kv, the peak power output drops to 200 kw, and the efficiency 
is reduced to 35 per cent. The lightly dashed lines are contours of constant efficiency. 
The dotted lines represent the deviation in frequency from a reference frequency 
indicated on the chart as Mc. The change in the oscillator frequency produced by a 



206 Introduction to Radar Systems [Sec. 6.2 

change in the anode current for a fixed load is called the pushing figure. In measuring 
the pushing figure the current must be changed rapidly in order to avoid frequency 
shifts due to temperature changes. The shaded areas of the chart correspond to regions 
of poor magnetron performance. 

The performance chart permits the radar designer to select the tube parameters 
which best satisfy the diverse requirements of a particular application. Although 
there is considerable variation in the performance charts for different magnetrons, the 
following general features seem to be shown by most magnetrons : (1 ) except for very low 
currents, increasing the anode current while maintaining the magnetic field constant 
results in a decrease in efficiency; (2) decreasing the magnetic field at constant current 
results in a decrease in efficiency; and (3) a drop in efficiency occurs at very small 
currents. In general, the performance chart indicates that large magnetic fields result 
in good efficiency. Although a large magnetic field requires a relatively heavy magnet, 
it may sometimes be the cheapest method of obtaining efficiency. 

The other plot of magnetron characteristics of interest in radar design is the Rieke 
diagram. The coordinates of the Rieke diagram are the load conductance and suscept- 
ance (or resistance and reactance). Plotted on the Rieke diagram are contours of 
constant power and constant frequency. Thus the Rieke diagram gives the power 
output and the frequency of oscillation for any specified load condition. Although a 
cartesian set of load coordinates could be used, it is usually more convenient to plot the 
power and frequency on a set of load coordinates known as the Smith chart. 12 The 
Smith chart is a form of circle diagram widely used as an aid in transmission-line 
calculations. A point on the Smith chart may be expressed in conductance-susceptance 
coordinates or by a set of polar coordinates in which the voltage-standing-wave ratio 
(VSWR) is plotted as the radius and the phase of the VSWR is plotted as the angular 
coordinate. The latter is the more usual of the two possible coordinate systems since 
it is easier for the microwave engineer to measure the VSWR and the position of the 
voltage-standing-wave minimum (or phase) than it is for him to measure the conductance 
and susceptance directly. The radial coordinate can also be specified by the reflection 
coefficient Y of the load since the VSWR p and reflection coefficient are related by 
the equation |T| = (p — l)/(/> + 1). The center of the Smith chart (Rieke diagram) 
corresponds to unity VSWR, or zero reflection coefficient. The circumference of the 
chart corresponds to infinite VSWR, or unity reflection coefficient. Thus the region of 
low standing-wave ratio is toward the center of the chart. The standing- wave pattern 
along a transmission line repeats itself every half wavelength ; therefore, 360° in the 
diagram is taken as a half wavelength. The reference axis in the Rieke diagram 
usually corresponds to the output terminals of the magnetron or the output flange of 
the waveguide. The angle in a clockwise direction from this reference axis is propor- 
tional to the distance (in wavelengths) of the standing-wave-pattern minimum from the 
reference point. An advantage of the Smith chart for plotting the effects of the load 
on the magnetron parameters is that the shapes of the curves are practically indepen- 
dent of the position of the reference point used for measuring the phase of the VSWR. 

An example of the Rieke diagram for a magnetron operating in the n mode is shown 
in Fig. 6.7. The contours of constant power approximate, in a rough manner, a set of 
circles, while the contours of constant frequency approximate arcs of circles which are 
almost perpendicular to the contours of constant power. The region on the chart 
where the contours of constant frequency crowd together is also the region where the 
output power is greatest. The frequency contours are farther apart in that region 
where the output power is low. Thus a given change in the phase of the VSWR will 
cause a greater change in the magnetron frequency if the operating point of the magne- 
tron is in the region of high-power output rather than in the region of low-power output. 
Therefore the greater the power output, the greater the efficiency, but the poorer the 



Sec. 6.2] 



Radar Transmitters 



207 



frequency stability. The phase and/or magnitude of the VSWR in a scanning radar 
might vary because the antenna sees a different load impedance, depending upon the 
objects it views. 

The location of the ATR tube can also affect the performance of the magnetron. 
At the start of the pulse, the ATR is unfired and presents an open circuit in the trans- 
mission line. If the location of the ATR is such that the phase of the VSWR causes the 
tube to operate in a favorable portion of the Rieke diagram (magnetron lightly coupled 



270' 




180° 



Fig. 6.7. Example of a Rieke diagram for the RK 6517/QK 358 /.-band magnetron. Solid curves 
are contours of constant power. Dashed curves are contours of constant frequency. Pulse width = 
3.2 /«ec, prf=391, duty cycle = 0.00125, average anode current = 62.5 ma d-c, peak anode 
current = 50 amp, and frequency = 1 ,250 Mc. {Courtesy Raytheon Company.) 

to the load), the starting characteristics of the magnetron will be enhanced. On the 
other hand, if the phase of the ATR reflection places the operating point in an un- 
favorable portion of the Rieke diagram, the starting characteristics will be poor. 

The region of highest power on the Rieke diagram is called the sink and represents 
the greatest coupling to the magnetron and the highest efficiency. Operation in the 
sink region is not always desirable since the RF spectrum of the magnetron output will 
tend to broaden, indicating a poor pulse shape. Also, the operation may be unstable 
because of mode changes. A change in the phase of the VSWR which moves the 
operating point of the magnetron into the low-power region (antisink) results in a 
lightly loaded magnetron. The build-up of oscillations in a lightly loaded magnetron 
is more ideal, and the magnetron pulses start more uniformly, than if the load were 
matched. However, a lightly loaded magnetron may perform poorly by showing signs 
of instability which take the form of arcing and an increase in the number of missing 



208 



Introduction to Radar Systems 



[Sec. 6.2 




Fig. 6.8. Single hole-and- 
slot resonator illustrating 
inductance tuning (L) and 
capacitance tuning (C). 



pulses. This poor operation results because the RF voltages 
inside the lightly loaded magnetron are large in the antisink 
region, making RF discharges more likely. 

An important characteristic of the magnetron is the pulling 
figure. It is a measure of the effect a change in the output 
load has on the frequency of oscillation. The pulling figure 
is defined as the difference between the maximum and the 
minimum frequencies of a magnetron oscillator when the 
phase angle of the load impedance varies through 360° and 
the magnitude of the VSWR is fixed at 1.5 (reflection co- 
efficient = 0.20). The pulling figure of a magnetron may 
be readily obtained from an inspection of the Rieke diagram. 
The difference between the minimum- and maximum- 
frequency contours intercepted by the circle corresponding 
to a VSWR = 1.5 is the pulling figure. For the magnetron 
whose Rieke diagram is shown in Fig. 6.7, the pulling figure is approximately 1.5 Mc. 
Tuning. The ability to tune a magnetron is a desirable operational feature. It is 
usually more difficult, however, to incorporate tuning into a magnetron than in other 
power tubes. A tunable magnetron permits the radar to be operated anywhere within 
a band of frequencies and to be set to a precise frequency, if desired. The latter 
property is not often available with fixed-tuned magnetrons whose frequencies might 
lie anywhere within a narrow band and are not under the control of the radar systems 
engineer. In some applications, such as the 
FM radar altimeter, it is absolutely essential 
that the transmitter be tunable over a wide 
range. The various methods for tuning a 
magnetron may be classified as (1) mechani- 
cal, (2) electronic, and (3) voltage-tuned. 
Mechanical tuning is accomplished by the 
movement of a tuning device; electronic 
tuning, by electronic beams or space charge 
located within the magnetron cavity or some 
external cavity; and voltage tuning is accom- 
plished by designing the magnetron to operate 
in a region where a change in anode voltage 
results in a change in frequency. 

In the mechanically tuned magnetron, the 
frequency of oscillation is changed by the 
motion of some element in the resonant circuit 
associated with the magnetron. Figure 6.8 
shows a single hole-and-slot resonator. The 
inductive tuning element L, when inserted into 
the hole of the resonator, changes the induc- 
tance of the resonant circuit by altering the 
surface-to-volume ratio in a high-current 
region. The change in inductance results in a change in frequency. A tuner that 
consists of a series of rods inserted into each cavity resonator so as to alter the induc- 
tance is called a sprocket tuner, or a crown-of-thorns tuner. All rods are attached to a 
frame which is positioned by means of a flexible-bellows arrangement as illustrated 
in Fig. 6.9. An inductance tuner can also be seen in the exploded magnetron of 
Fig. 6.4. The insertion of the rods into each anode hole decreases the inductance of 
the cavity and therefore increases the resonant frequency. One of the limitations of 




Cavity 



Fig. 6.9. Example of an inductance-type 
tuner. {Courtesy Raytheon Company.) 



Sec. 6.2] 



Radar Transmitters 



209 



inductive tuning is that it lowers the unloaded Q of the cavity and the efficiency of the 
tube. 

The insertion of an element C into the cavity slot as shown in Fig. 6.8 increases the 
slot capacitance and decreases the resonant frequency. Because the gap is narrowed 
in width, the breakdown voltage will be lowered, and capacity-tuned magnetrons must 
usually operate with low voltages and hence low powers. A common form of capacity 
tuner is called the cookie cutter (Fig. 6. 10). It consists of a metal ring inserted between 
the two rings of a double-ring-strapped magnetron, thereby increasing the strap 
capacitance. Because of the mechanical- and voltage-breakdown problems associated 
with the cookie cutter, this tuner is more suited for use at the longer wavelengths. 

Both the capacitance and the inductance 
tuners described above are symmetrical. Each 
cavity is affected in the same manner, and the 
angular symmetry of the n mode is preserved. 

A 10 per cent frequency change can be ob- 
tained with either of the two tuning methods 
described above, although there is some in- 
dication that the cookie cutter is more restricted 
in tuning range than the crown-of-thorns tuner. 
The two tuning methods may be used in com- 
bination to cover a larger tuning range than 
is possible with either one alone. Tuning 
ranges of 1.5 to 1 are not uncommon with this 
arrangement. Tuning rates of 100 Gc/sec have 
been achieved with servo-controlled, mechani- 
cally tuned magnetrons. 

A limited tuning range, of the order of 1 per 
cent, can be obtained rather simply by means 
of a screw inserted in the side of one of the 
resonator holes. This type of adjustment is 
useful when it is desired to fix the magnetron 
frequency to a specified value within the normal 
scatter band of untuned magnetrons. A tuning 
mechanism in only one resonator hole does 
not, as a rule, preserve angular symmetry 
and is a form of unsymmetrical tuning. 

Another form of unsymmetrical tuning is an auxiliary resonant cavity coupled to one 
of the magnetron cavities. The auxiliary cavity is tightly coupled and determines the 
operating frequency of the magnetron. The frequency of the auxiliary cavity may be 
changed by making one wall of the cavity flexible so that it can be moved in or out. A 
tunable magnetron, using a section of a double- ridged waveguide as an auxiliary 
tuning cavity whose resonant frequency was varied by adjusting a short-circuiting 
plunger located at one end of the cavity, could be tuned over the frequency range from 
9,000 to 9,600 Mc with a peak power output of 140 kw. 13 

A fixed-frequency magnetron also may be tuned over a limited frequency range of 
about 1 per cent by varying the load into which the magnetron operates. A single-stub 
tuner located external to the tube may be used for this purpose. A change in the 
impedance of the single-stub tuner changes the operating point on the Rieke diagram 
and therefore changes the frequency. 

An electron beam injected into one or more of the cavities of a magnetron will change 
the effective dielectric constant of the cavity and thereby change the frequency. 14 - 15 
The electron beam may be inserted directly into the magnetron cavity in a region of high 




Anode 
segment 

"■Heavy dark line represents tuner- 
ring position between the magnetron straps 

Fig. 6.10. Example of capacitance-type 
tuner. (Courtesy Raytheon Company.) 



210 Introduction to Radar Systems [Sec. 6.2 

RF electric field, or an external cavity may be used with an electronic beam or a control- 
lable space charge formed by a magnetron diode. The frequency is varied by electrically 
varying the density of the electronic beam. Electronic tuning is probably more 
appropriate to CW magnetrons such as might be used for FM altimeters or for micro- 
wave communications. This technique has been used to frequency-modulate a 
4,000-Mc CW magnetron 16 with a frequency deviation of 2.5 Mc (total frequency 
swing of 5 Mc). Larger frequency deviations are possible if some amplitude modula- 
tion can be tolerated. The power output from this tube was 25 watts, with an efficiency 
of 50 per cent. 

Electronic tuning has also been applied to a relatively high power CW magnetron. 17 
Electron beams were injected into 9 of the 12 cavities of a vane-type magnetron. At 
900 Mc a frequency deviation of 3.5 Mc was obtained with a power output of 1 kw and 
an efficiency of 55 per cent. The tube was also mechanically tuned over the frequency 
range of 720 to 900 Mc with a cylindrical element which varied the interstrap capaci- 
tance. 

It was mentioned previously that the magnetron frequency will vary if the anode 
current or voltage is varied. This is known as frequency pushing, and in most magnetron 
applications it is not a desirable characteristic. This phenomenon can be used to tune 
a magnetron, but with space-charge-limited current, only a few per cent change in 
frequency can be obtained by changing the current. However, under certain con- 
ditions of operation the magnetron frequency may be made quite sensitive to voltage 
changes. It has been found possible in some cases to tune magnetrons over a frequency 
range of 4: 1 by means of voltage tuning. 15 * 18 . 19 

The necessary conditions for voltage tuning are that the magnetron be heavily loaded 
and that the anode current be limited and not increase with an increase in anode 
voltage. This latter condition is usually met by operating the cathode with the electron 
emission temperature-limited rather than space-charge-limited. The number of 
electrons in the interaction space may also be limited by providing a region of cathode 
surface which is nonemitting. The voltage-tuned magnetron therefore acts as a 
constant-current generator. 

When the anode circuit is heavily loaded and the number of electrons in the inter- 
action space is restricted, as required for voltage tuning, the anode circuit does not 
determine the frequency of oscillation, but it does determine, in part, the RF power 
output. 

Voltage tuning results in a considerably greater frequency change than does frequency 
pushing for the same change in anode voltage. Typical voltage-tuning characteristics 
show a change of frequency of 0.1 to 2 Mc/volt. The frequency is usually a linear 
function of the anode voltage, but the power output will not be constant over the tuning 
range. The voltage-tuned magnetrons which have been reported in the literature 18 - 20 ' 21 
have been low-power CW tubes with power outputs of the order of a few watts or tens 
of watts, although the first voltage-tuned magnetron generated about 100 watts. The 
tuning range of these tubes covers a two-to-one frequency band, but their efficiencies are 
lower than conventional magnetrons. Most of these tubes have an interdigital- 
resonant-cavity or split-anode structure. 

The voltage-tuned magnetron seems more suitable to low-power, rapid-tuning 
applications than as a high-power radar transmitter. It might be applicable to a 
low-power FM-CW radar such as the altimeter or as a local oscillator in a wide-tuning- 
range receiver. 

Ferrite materials might be used to tune an interdigital magnetron. A ferrite cylinder 
can be placed near the shorted end of a coaxial line which is coupled to the interdigital 
resonator. The ferrite material is kept out of the main magnetic field of the magnetron 
so that its permeability may be controlled by means of its own biasing magnetic field. 



Sec. 6.2] Radar Transmitters 211 

A variation of permeability in the coupled coaxial line results in a change of frequency. 
It is claimed that theoretical calculations show that a tuning range of 5 to 10 per cent 
may be expected. 22 

Long-line Effect. 1 ' 11 ' 23 ' 25 The Rieke diagram of Fig. 6.7 indicates that a change in 
the phase of the VSWR can seriously affect the operation of a magnetron, especially 
if the magnitude of the VSWR is large. Changes in the phase of the VSWR occur if 
the load into which the magnetron operates changes or if the frequency of oscillation 
varies. If the VSWR magnitude is large, a tunable magnetron might encounter poor 
operation at certain frequencies where the VSWR phase places the magnetron operat- 
ing point in an undesirable portion of the Rieke diagram. The phase angle associated 
with the two-way propagation along a transmission line of length L is (f> = 4-rrLflc, 
where / is the frequency of oscillation and c is the velocity of propagation. The 
change in phase A<£ for a particular change in frequency A/ is equal to 4nL Af/c. 
The phase change is proportional to the length of the line as well as to the change in 
frequency. The longer the transmission line, the greater will be the phase change and 
the more likely it will be that the magnetron operating point will be in, or pass through, 
a region of poor magnetron operation. The poor magnetron performance caused 
by a change in VSWR phase when the magnetron is connected via a long length 
of transmission line to a mismatched load with large VSWR is called the long-line 
effect. 

The long-line effect causes the tuning curve (plot of frequency vs. tuner position) of a 
tunable magnetron to be altered. There may even be periodically spaced holes in the 
tuning curve where it is not possible for the magnetron to oscillate. The long-line 
effect may also result in a poor spectrum (poor pulse shape), missing pulses, and fre- 
quency jumping. The modulation characteristics of frequency-modulated tubes might 
also be distorted. The long-line effect is not a characteristic of the magnetron alone. 
It is a property of any self-excited oscillator whose frequency is affected by the output 
impedance. 

The long-line effect results from the influence of the wave that has traveled to the end 
of the transmission line, has been reflected there, and has returned to the magnetron. 
It depends, in part, on the length of the pulse and is different with a CW tube than with a 
pulsed tube. It is not present in a transmission line whose two-way transit time exceeds 
the length of the pulse since the tube will not be on when the reflection returns. Thus 
long-line effect is absent if the line is sufficiently long. For this reason, the phe- 
nomenon has sometimes been referred to as the short-line effect, although the term 
long-line effect seems to be more generally accepted. 

Examples of the manner in which the long-line effect alters the tuning curve of a 
pulsed magnetron are shown in Fig. 6.11a to c. The ordinate is the magnetron fre- 
quency, and the abscissa is the position of the tuning mechanism of the magnetron. 
The straight-line curve illustrated in Fig. 6.1 la corresponds to a transmission line per- 
fectly terminated in a reflectionless load. The effect of a small mismatch is shown in 
Fig. 6.11*, and a large mismatch, in Fig. 6.11c. With a small mismatch as in Fig. 6.116, 
the spectrum of the magnetron might be abnormally broad over those parts of the 
tuning curve where the slope is nearly vertical. The tuning curve for large mismatch 
(Fig. 6.1 lc) has regions where more than one frequency is indicated for a given tuner 
setting. Operation at more than one frequency for a given tuner setting is not possible. 
As the tuner setting is increased, the frequency of oscillation will increase uniformly 
until point 1 is reached. The frequency then jumps discontinuously to point 3. 
Frequencies in between, such as point 2, are not obtained. Thus there will be holes in 
the frequency coverage when the mismatch is severe. The frequency difference 
between alternate points where the tuning curve with mismatch crosses the tuning 
curve with no mismatch (dashed curve) is |(r/L)(A//l 9 ), where c is the velocity of light, L 



212 Introduction to Radar Systems [Sec. 6.2 

is the length of the line, X is the wavelength in free space, and X g is the wavelength in the 
guide or the transmission line. 

Pritchard 24 has shown that the longest length of transmission line, L e , for which 
completely stable operation of the tube occurs, regardless of the phase angle of the load, 
is given by 

where L c = skip length, or critical length 

P F = pulling figure of magnetron 

p = voltage-standing-wave ratio 




Tuner position X 
(c) 



Tuner position X 
id) 



Fig. 6.11. Magnetron tuning curves, (a) Perfectly terminated transmission line (no mismatch); 
(b) small mismatch; (c) large mismatch; (d) large mismatch, CW magnetron. 

If the skip length is measured in feet, the pulling figure measured in megacycles, 
Eq. (6.1) may be written 

L c (ft) = -^- (6.2) 

P F (P - 1) 

The above expressions for the critical line length assume a lossless transmission line. 
The effect of loss is to reduce the amplitude of the reflected wave, thereby reducing the 
VSWR (at the input to the line) and the long-line effect. A reduction of the VSWR 
seen by the tube increases the allowable skip length. Pritchard shows that the maximum 
VSWR p L which can be tolerated at the end of the transmission line is given by 

_ {(kjX g )l(L c IX g ) + if + (klk g )l(2L c IK) sinh [(2aA„)L c /Vl 
1 - {klX a )j{LJX g ) sinh 2 [(a^)L e /AJ 



Radar Transmitters 



213 



Sec. 6.2] 

where k\X Q = <fiAnin)(flP F XW 

a. = transmission-line attenuation per unit length 

/= frequency 
This equation is plotted in Fig. 6.12 for representative values of the parameters with 
several waveguide sizes, and for a = 0. For any lossy line, no matter how small the 
losses, Eq. (6.3) shows that there will always be some length of line for which large 
VSWRs (essentially infinite) can be tolerated. This length can be calculated by setting 
the denominator of Eq. (6.3) equal to zero and solving for L c . It is of little practical 
significance, however, since the loss may be prohibitively high. 



2.2 



2.0 



1.6 



|l.4 



1.2 



1.0 



1 — I Mill 




H 1 — I I I I I I 



J ' 



10 



100 



1,000 
Normalized line length, 



10,000 



100,000 



Fig. 6.12. Plot of the maximum VSWR p L as a function of line length for representative values of 
parameters with several waveguide sizes, and for a = 0. (From Pritchard, u IRE Trans.) 

Although a tunable pulse magnetron has been assumed in the above discussion of 
the long-line effect, the fixed-tuned magnetron may also be adversely affected by the 
presence of a large VSWR and a long transmission line. The location of the breaks in 
the tuning curve varies uniformly with the phase of the reflection. Therefore a variation 
of the load which causes a change in the phase of the VSWR may shift the entire tuning 
curve and might cause an unstable region to be shifted to the frequency of the fixed- 
tuned magnetron. 

The curves in Fig. 6.1 la to c apply to a pulsed magnetron. The behavior of the 
tuning curve of a CW magnetron with a long transmission line differs from that of the 
pulse magnetron because of frequency hysteresis. An example of the long-line effect 
on the tuning curve of a CW magnetron is shown in Fig. 6. 1 1 d. In the CW magnetron 
there are two different frequencies possible for a given frequency setting, both of which 
are stable. One frequency is obtained when the tuner setting is increased, the other 
when the tuner setting is decreased. The dashed portions of the curve correspond to 
frequency jumping. In the CW case there are inaccessible frequencies just as with the 
pulse magnetron, but the percentage of inaccessible frequencies is less. 

An obvious method of eliminating the long-line effect is to avoid the use of long 
transmission lines by locating the transmitter directly at the antenna terminals. How- 
ever, not all radar transmitters are small enough to be located at the feed of a reflector- 
type antenna. It is easier to mount a given transmitter at the feed of a lens antenna 



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<5 EC . 6.2] Radar Transmitters 215 

since aperture blocking is not a problem (Sec. 7.6). Another antenna technique which 
avoids long lengths of transmission line is the Cassegrain reflector geometry (Sec. 7.5). 
The long-line effect may also be eliminated if the transmission line is longer than one- 
half the pulse length or if the attenuation in the line is sufficiently large. The deliberate 
use of a transmission line with large attenuation is not efficient and would be of little 
value for high-power radar transmitters. 

In those applications where it is not possible to locate the transmitter directly at the 
antenna or to use a transmission line longer than one-half the pulse length, the reflected 
wave from the load can be eliminated at the magnetron with a unilateral device such as 
an isolator or a circulator. These devices prevent the energy reflected from the 
mismatched load from returning to the magnetron, but they permit the energy to flow 
unimpeded in a forward direction from the magnetron to the load. 





Fig. 6.13. Photograph of type 7182 magnetron, without electromagnet. {Courtesy English Electric 
Valve Co., Ltd.) 

Another technique for reducing the long-line effect is to decouple the magnetron to 
reduce its pulling figure. Equation (6.1) shows that a reduction of the pulling figure 
results in an increase of the skip length of the line. Decoupling the oscillator results in 
a decrease in efficiency, as does the insertion of loss in the transmission line. There will 
usually be less over-all loss in efficiency for a given increase in skip length by decoupling 
the magnetron than by the deliberate insertion of loss. 

If the VSWR is not too high, a phase shifter might be used to shift the entire tuning 
curve to permit quasi-stable operation in between the points of frequency jump. This 
will not be practical if the frequency separation between "skips" is small. 

An oscillator followed by a power amplifier such as a klystron will not experience 
long-line effect because of the isolation provided by the amplifier. On the other hand, 
an Amplitron following an oscillator will not eliminate the long-line effect since energy 
traveling in the reverse direction suffers little or no attenuation. 

Examples of Pulse Magnetrons. Table 6. 1 lists the characteristics of five magnetrons 
covering the frequency range from L band to Xband. The tubes included in this table 
are not necessarily the best, nor are they claimed to be typical of the many magnetrons 
which may be available. The tubes were selected since they illustrate the parameters 
and characteristics of magnetrons. The selection of a magnetron for a specific applica- 
tion is a job that requires careful examination of the various types available from the 
several manufacturers in this country as well as abroad. All the tubes in Table 6. 1, 
with the exception of the C-band tube, are relatively high power tubes. The C-band 
tube is included since it was designed specifically for a commercial application (airborne 
weather-avoidance radar), where long life is a prime requirement. The tubes are all 
fixed-tuned. 



216 Introduction to Radar Systems 



[Sec. 6.3 



Most of the terms listed in the table have been 
defined previously except for the stability and the 
thermal factor. The stability is a measure of the 
percentage of missing pulses. A missing pulse 
is usually defined as one whose energy is 30 
per cent less than normal. The reduced energy 
may be due to a lower-than-normal amplitude, 
shorter pulse width, or incorrect frequency. 
The thermal factor is a measure of the frequency 
change produced by a given change in anode 
temperature. 

The English Electric Valve Co. type 7182 S- 
band magnetron is of a radically different design 
from the usual magnetron. 26 A photograph of 
the type 7182 without magnet is shown in Fig. 
6.13, and a cross section illustrating the features 
of a 5-Mw version is shown in Fig. 6.14. The 
length of the anode is two to three times that 
of ordinary designs, permitting cathodes large 
enough to dissipate the back-bombardment 
power generated by electrons returning to the 
cathode. Instead of coupling the output power 
through the side of one of the cavities, it is 
coupled out symmetrically from one end. A 
symmetrical output allows stable operation in the 
77 mode without the need for strapping. The 
long anode plus the symmetrical output makes 
it natural to use a solenoid electromagnet. An 
outstanding characteristic of this design is its 
long life, which is an order of magnitude better 
than conventional magnetrons of equivalent 
power. 
The examples given in Table 6. 1 are relatively high power magnetrons. However, 
one of the largest fields of application for magnetrons is in marine radars, where small 
power tubes are widely used. A typical Jf-band marine radar might employ a fixed- 
tuned magnetron generating 5 kw of peak power with an average power of 5 watts, 
operating at a voltage of 5 kv and weighing 4 lb complete. 32 

6.3. Klystron Amplifier 

The klystron amplifier overcomes the high-frequency limitations of conventional 
grid-controlled tubes by using to good advantage the transit-time phenomena in the 
electron beam. The velocity of the electrons constituting the electron beam in the 
klystron amplifier is modulated by the input signal. The resulting velocity modulation 
is converted into density modulation. A resonant cavity extracts the RF power in the 
density-modulated beam and delivers it to a useful load. 

The klystron amplifier has had important application as a radar transmitter and 
fulfills a need which cannot be supplied by self-excited oscillators like the magnetron. 
The chief advantage of the klystron amplifier which makes it attractive as a radar 
transmitter is that it is capable of large, stable output power with good efficiency and 
high gain. Because it is basically a power amplifier, it can be driven by a stable crystal- 
controlled oscillator followed by a frequency-multiplier chain. This arrangement 
results in more stable operation than is possible with a self-excited power oscillator, and 




Heater connection 



Cothode and heater 
connection 



^Locating ond 
/ retaining flonge 



Heoter 



Cothode 



Anode 



Aerial plate 



choke 



Output window 



Fig. 6.14. Cross section illustrating the 
major features of a 5-Mw version of the 
E.E.V. magnetron. (Courtesy English 
Electric Valve Co., Ltd.) 



Sec. 6.3] 



Radar Transmitters 217 



hence better MTI performance. Stable RF generators such as the klystron are almost 
always preferred in modern MTI radars whenever operational conditions permit. 

In a klystron the RF input is well isolated from the RF output, and high, stable gains 
are possible from a single "bottle." Gains of from 30 to 40 db are usual in a three- 
cavity tube, and gains exceeding 80 db are possible, depending upon the number of 
cavities. Large gains mean that a low-power oscillator can be used as the input. The 
d-c and the RF portions of the tube are separate in the klystron. The cathode and 
collector regions may therefore be designed to perform their respective functions in an 
optimum manner without concern for their effect on the RF fields. As a result, the 
life of a klystron may be made as good as or better than the life of other types of micro- 
wave power generators. 



RF cavities 



Heater 




Interaction gaps 
Collector-^. 



Modulating 
anode 



Fig. 6.15. Diagrammatic representation of the principal parts of a three-cavity klystron. 

The chief limitations of klystrons are their relatively large size and high operating 
voltages. Large size is better suited to ground-based installations. The voltages 
required can be greater than 100 kv, necessitating special high-voltage handling 
techniques. High voltage produces X-ray radiation in the vicinity of the tube, so that 
lead shielding must be provided to protect operating personnel. 

Description of Operation. A sketch of the principal parts of the klystron is shown in 
Fig. 6. 1 5. At the left-hand portion of the figure is the cathode, which emits a stream of 
electrons. A conservative value of maximum emission density for short-pulse, long- 
life operation of klystrons is about 5 amp/cm 2 . The portion of the tube which focuses 
the electrons into a beam is called the electron gun. A modulating anode is usually 
included as part of the electron-gun structure to provide a convenient means for 
pulsing or modulating the electron beam. The RF cavities which correspond to the 
LC resonant circuits of lower-frequency amplifiers alsoserveas the anode since they are 
at a positive potential with respect to the cathode. The positive potential applied to 
the cavities is called the beam-accelerating voltage, or anode voltage. Electrons are 
not intentionally collected by the anode as in other tubes; instead, the electrons are 
terminated by the collector electrode (shown on the right side of the diagram) after the 
beam has given up its RF energy to the output cavity. 

The RF voltage of the input signal is applied across the interaction gap of the first 
cavity. Low-power tubes might contain a grid structure at the gap to provide coupling 
to the beam. However, the gap in high-power tubes does not usually contain a grid 
because of its poor power-handling capability. The absence of a grid does not seriously 
impair the coupling between the gap and the beam. Those electrons which arrive at 
the gap when the input voltage is at a maximum (peak of the sine wave) experience a 
voltage greater than the average and will be accelerated to a higher velocity than those 
electrons which arrive at the gap when the RF input is at a minimum (trough of the sine 



218 Introduction to Radar Systems [Sec. 6.3 

wave). The process whereby a time variation in velocity is impressed upon the beam 
of electrons is called velocity modulation. 

In the drift space, or tunnel, those electrons which are speeded up during the peak of 
one cycle catch up with those electrons slowed down during the previous cycle. The 
result is that the electrons of the velocity-modulated beam are "bunched," or density- 
modulated, after traveling through the drift space. If the interaction gap of the output 
cavity were placed at the point of maximum bunching, power could be extracted from 
the density-modulated beam. Most high-power klystrons for radar application have 
one or more cavities between the input and the output cavities to provide additional 
bunching, and hence higher gain. The intermediate cavities are not fed with energy 
from the outside. In the three-cavity klystron the second cavity may be tuned to the 
frequency of oscillation, or even a slightly higher frequency for greater efficiency. 
After the bunched electron beam delivers the RF power to the output cavity, the electrons 
are collected by the collector electrode which is at, or slightly below, the cathode 
potential. Power is extracted from the output cavity to the load by a coupling loop, or 
if a waveguide output is used, by means of an iris. 

In order to counteract the mutual repulsion of the electrons which constitute the 
beam, an axial magnetic field (not shown in Fig. 6.15) is generally employed. The 
magnetic field confines the electrons to a beam and prevents them from dispersing. 
The optimum magnetic field strength is fairly critical and is not necessarily uniform 
along the length of the tube. In some klystrons the electron beam may be confined by 
electrostatic fields designed into the tube structure and external magnets are not 
required. In low-power CW tubes the beam might even be focused by positive-ion 
space charge. If the beam were not properly confined in a high-power klystron, the 
stray electrons would impinge upon the metal structure of the tube and cause it to 
overheat or possibly be destroyed. 

Not all the power available in the klystron beam is delivered to the load. An 
example of the division of power in the Sperry SAS-37 klystron was reported by 
Learned and Veronda for a 200- watt CW amplifier, operating at a frequency of 2,450 
Mc, utilizing grids at the RF interaction gaps and employing positive-ion focusing. 33 
Of the total d-c power in the electron beam, only 41 per cent is converted to RF power. 
Of the 59 per cent not converted, 41 per cent is dissipated at the collector while 18 per 
cent is lost in the drift tube. (Less power would be lost in a klystron without grids.) 
Of the 41 per cent converted to RF power, only 25 per cent is delivered to the load. 
RF losses in the output cavity account for 4 per cent, transit-time loading accounts for 
6 per cent, while the production of secondary electrons with virtually zero velocity 
accounts for an additional 6 per cent. Thus the RF conversion efficiency of this 
particular tube is 25 per cent (which is low for klystrons). The over-all efficiency 
would have to include the heater power, power required for cooling, and power to 
generate the magnetic focusing field if focusing is accomplished magnetically. RF 
conversion efficiencies of practical high-power klystrons seem to lie within the range of 
35 to 45 per cent. 

The advantage of the klystron over other microwave tubes in producing high power 
is due to its geometry. The regions of beam formation, RF interaction, and beam 
collection are separate and independent in the klystron. Each region can be designed 
to best perform its own particular function independently of the others. For example, 
the cathode is outside the RF field and need not be restricted to sizes small compared 
with a wavelength. Large cathode area and large interelectrode spacings may be used 
to keep the emission current densities and voltage gradients to reasonable values. The 
only function of the collector electrode in the klystron is to dissipate heat. It can be of 
a shape and size most suited for satisfying the average or peak power requirements 
without regard for conducting RF currents, since none are present. 



Sec. 6.3] Radar Transmitters 219 

The design flexibility available with the klystron is not present in other tube types 
considered in this chapter, except for the traveling-wave tube. In most other tubes the 
functions of electron emission, RF interaction, and collection of electrons usually occur 
in the same region. The design of such tubes must therefore be a compromise between 
good RF performance and good heat dissipation. Unfortunately, these requirements 
cannot always be satisfied simultaneously. Good RF performance usually requires 
the tube electrodes to be small compared with a wavelength, while good heat dissipation 
requires large structures. 

The high-power capability of the klystron, like anything else, is not unlimited. One 
of the major factors which has restricted the power available from klystrons has been 
the problem of obtaining RF windows capable of coupling the output power from the 
vacuum envelope to the load. Other factors limiting large powers are the difficulty of 
operating with high voltages, of dissipating heat in the collector, and of obtaining 
sufficient cathode emission current. 

External and Internal Cavities. Two types of resonant cavities have been employed 
in klystrons. They differ in being within or outside the vacuum envelope of the tube. 
The resonant tuning cavities may be placed external to the vacuum by sealing the 
interaction gap with a suitable low-loss vacuum-tight insulator. This is called a 
window and is usually ceramic. Cavities external to the vacuum system are easier to 
tune and maintain. In practice the tuning range of external cavities might be twice 
that of similar cavities tuned from within the vacuum. 

When the cavities are wholly within the vacuum envelope, only an input and an 
output window are required for the tube and they need not be placed directly at the 
interaction gap. By contrast, the tube with external cavities requires a window at 
each cavity. When the output window must be placed at the interaction gap, as in the 
case of externally tuned cavities, the inside of the ceramic window may be bombarded 
by secondary electron emission emanating from the downstream tip of the output gap. 
The output window can become overheated and fail. This heating is in addition to the 
RF heating due to the dielectric losses in the ceramic when transmitting RF power. 
Dielectric heating occurs in the windows of both external and internal cavities. 

External cavities are often preferred because of their wider tuning range and more 
convenient method of tuning whenever the output window does not limit the power- 
handling capability of the tube. However, internal cavities are probably more 
suitable at the higher frequencies. 

Modulating Anode. Three possible methods of pulsing a klystron are by turning on 
and off (1) the klystron-beam accelerating voltage, (2) the RF input signal, or (3) the 
klystron-beam current. The last mentioned is controlled by an electrode in the 
electron gun called the modulating anode. 

When the beam is pulsed by turning the accelerating voltage on and off, the entire 
beam current must be pulsed as well. This is similar to plate modulation of a triode or 
magnetron, and it requires a modulator capable of handling the full power of the beam. 
In method 2, the beam current should also be modulated when the RF input signal is 
modulated; otherwise beam power will be dissipated to no useful purpose in the 
collector in the interval between RF pulses, and the efficiency of the tube will be low. 
Of the three methods, the modulating anode requires the least modulating power. 
The only control power necessary is the very small amount required to charge and 
discharge the capacitance of the klystron gun and its associated circuitry, and this is 
independent of the pulse length. In one design, the peak pulsed modulating power is 
less than \ per cent of the peak input power. 34 Hard vacuum tubes may be used in the 
pulse modulator, minimizing any time jitter. Also, the phase shift between the RF 
input and the RF output of the klystron will not change to any significant degree as 
voltage is applied to the modulating anode. 



220 Introduction to Radar Systems [Sec. 6.3 

The cutoff characteristics of the modulating anode permit only a few electrons to 
escape from the electron gun during the interpulse period when the beam is turned off. 
This is important in radar application since the receiver sensitivity will be degraded if 
sufficient electrons are present during the interpulse period to cause the stray electron 
current noise to exceed receiver noise. 

The modulating characteristics (output RF voltage vs. modulating anode voltage) 
of the modulating anode can be made linear over a portion of the operating range so 
that the output waveform may be shaped as desired. An important application of 
pulse shaping is in air navigation systems such as Tacan, where it is necessary to transmit 
a pulse with as little sideband energy as possible in order to avoid interference between 
adjacent or nearby channels. In such applications a Gaussian-shaped pulse is preferred 
since its spectrum falls off rapidly, resulting in reduced sideband energy. The Gaussian- 
shaped pulse may be readily approximated with the modulating-anode technique. 35 . 36 
A Gaussian-shaped pulse may also be desired in radar applications in which interference 
to nearby radar receivers at slightly different frequencies may be more important than 
the loss in range accuracy and resolution obtained when a Gaussian pulse is used instead 
of a rectangular pulse. 

Examples of High-power Klystrons. Although the principle of the klystron was 
demonstrated by several investigators during the late 1930s, credit for its invention is 
usually given to the Varian brothers. 37 The klystron was based on the pioneering 
ideas of W. W. Hansen concerning the interaction of electron beams and resonant 
microwave cavities. The Varian klystron actually preceded the magnetron invented 
by Randall and Boot, but the potentialities of the klystron for high power were not 
exploited until after the war. 

Many experimental klystrons were built during the late thirties, but the incentive in 
the United States for a high-power microwave tube suitable for radar application was 
not as great as in Great Britain, where they were more directly involved at that time in 
thwarting aggression. Consequently, when the plans for the British magnetron were 
made available to the United States in 1940, the magnetron, rather than the klystron, 
became the basic RF power generator for radar transmitters. The failure to press the 
development of the high-power klystron during the war was due in large part to the war- 
time necessity of concentrating the relatively scarce technical efforts in a limited number 
of fields. 

However, a considerable effort was concentrated, in the United States, on the 
relatively low power reflex klystron for use as local oscillators in microwave super- 
heterodyne receivers. The efficiency and power output of the reflex klystron is too low 
to be of consequence for high-power radar transmitters. The reflex klystron may be 
used, however, in low-power short-range radars, where efficiency is not too important. 

As is true of many devices which prove to be of practical value, the potential worth of 
the klystron as a high-power microwave generator was first demonstrated by the 
university scientist as a by-product of his pursuit of fundamental knowledge, rather 
than by the systems engineer. The first high-power klystron tube capable of megawatts 
of peak power was operated at Stanford University in March, 1949, and was developed 
for use in a linear accelerator. 38 It was designed to operate at a frequency of 2,857 Mc 
in-the 5 band and could be tuned over a frequency range of 100 Mc with a' flexible 
diaphragm which constituted one wall of a cavity. The tuning mechanism and the 
cavity resonators were located within the vacuum envelope. These tubes developed a 
peak power of 20 Mw at an efficiency of 35 per cent. They have also been operated 
with 30 Mw of peak power and at an efficiency of 43 per cent, but at a sacrifice in tube 
life. The peak power was greater than that delivered by any other tube at any frequency. 
The largest pulsed klystron power before the development of these tubes had been 
about 30 kw and was achieved by the British during the war. 



S EC . 6.3] Radar Transmitters 221 

The pulse width of the Stanford tube was 2 fisec, and the pulse repetition frequency, 
60 cps, corresponding to an average power of 2.4 kw when the peak power was 20 Mw. 
A three-cavity design was used, and the power gain was 35 db. The tube could operate 
with a maximum beam accelerating voltage of 400 kv and a maximum peak current of 
250 amp, although typical operating values were 325 kv and 185 amp. Pumping had 
to be employed to maintain the vacuum during operation. A voltage of 400 kv 
represents a practical upper limit for accelerating voltages, not only because of the 
difficulties in working with large voltages, but be- 
cause of the onset of relativistic effects. At higher 
accelerating voltages the electron velocity is close 
to that of light. Further increase in voltage 
results in an increase in electron mass rather than 
velocity. 

Twenty-two of these klystrons were used at 
Stanford University in the 220-ft linear acceler- 
ator to produce electrons with energies in the 
vicinity of 1 billion volts. In operation, these 
tubes have had an average life of approximately 
1,500 hr. 

The development of the Stanford 30-Mw 
klystron represented a considerable achievement 
and opened new possibilities for the radar 
systems engineer. In particular, it permitted the 
development of MTI radar systems far better 
than was possible with the magnetron. The 
superior average power capabilities of the klys- 
tron permitted radars to be designed with con- 
siderably more power than possible previous to 
its introduction. 

The pioneering work of the Stanford scientists 
was followed by the engineering and packaging 
of sealed-off klystrons by the tube industry. The 
first two klystrons commercially available for 
radar application were the Sperry Gyroscope 
Company SAL-36 and the Varian VA-87. The 
Sperry SAL-36 39 - 40 operated at L band with 2 to 
4 Mw of pulsed power with an efficiency exceed- 
ing 40 per cent. The VA-87 delivered nominally 
1 Mw of peak power at S band. The SAL-36 
is a three-cavity amplifier, while the VA-87 has four cavities. 

A photograph of the VA-87 is shown in Fig. 6.16. It is a four-cavity tube with a 
synchronously tuned saturation gain of about 61 db and a synchronously tuned large- 
signal bandwidth of about 20 Mc. In normal operation the tube is tuned for 
maximum power output with a beam voltage of 90 kv and an RF input of only 2.5 watts. 
The half-power bandwidth under these conditions of operation is about 27 Mc, and the 
gain is 57.6 db. The pulse-to-pulse phase jitter of the VA-87 is less than £° within 
any 4-msec period. It weighs 65 lb and requires a 235-lb magnet assembly. 

The Stanford tube scientists also developed a family of sealed-off klystrons suitable 
for radar application. 41 These were based on the principles learned from the 30-Mw 
tube. They operate in the L, S, and X bands at pulse powers of 3.2, 2.0, and 1 .2 Mw, 
respectively. The basic design has apparently been incorporated in commercially 
available tubes. 




Fig. 6.16. Varian VA-87 pulsed-amplifier 
klystron. (Courtesy Varian Associates.) 



222 Introduction to Radar Systems 



[Sec. 6.3 



One of the largest klystrons, both physically and in terms of average power is the 
Eitel-McCullough X626 pictured in Fig. 6.17. The average power from this tube is 
75 kw « It stands 10 ft 6 in. high and weighs 800 lb, exclusive of auxiliary equipment 
The tube is designed for very long range radars. It delivers a relatively long pulse of 
2 msec at a 30-cps pulse repetition frequency. The peak power is 1 .25 Mw, and the 
duty factor is 0.06. The conversion efficiency is 43 per cent. The tube utilizes three 
cavities external to the vacuum system. The gain is 30 db, and the tuning range is from 
400 to 450 Mc. The electron-gun portion of the tube is operated immersed in about 
800 gal of oil, while the other parts of the tube are water-cooled. From 1,000 to 4 000 




Fig. 6.17. Eimac X626 pulsed-amplifier klystron. {Courtesy Eitel-McCullough, Inc.) 

lb of lead surrounds the tube in order to protect operating personnel from X-ray 
radiation. A tube with similar characteristics, but with internal rather than external 
cavities, was also developed by the Varian Associates and is known as the VA-842. 

Even though the power output of the X626 klystron is large by any standards, it has 
been claimed (Ref. 42, p. 3) that "the design of a tube to handle 10 to 15 times the'power 
of the X626 would be a relatively straightforward (but not small) task." 

The klystron tubes described above all require external electromagnets to confine the 
electrons to a beam. It is also possible in some applications to use electrostatic 
space-charge forces to focus the beam. With electrostatic focusing the electron beam 
is first made to converge and then is allowed to diverge. The microwave cavities must 
be especially designed to operate with this type of beam. The drift spaces in a klystron 
with space-charge focusing are short and of large diameter. The interaction gaps are 
usually gridded to minimize stray coupling between the RF fields of the cavities and to 
give efficient interaction between the RF fields and the beam. Because of these 



Sec. 6.3] 



Radar Transmitters 



223 



restrictions the power output of space-charge-focused tubes has not been as large as 
with electromagnetic focusing. 

An example of an electrostatic space-charge-focused klystron amplifier is the SAL-89 
developed by the Sperry Gyroscope Company. 43 This is a three-cavity tube covering 
the frequency band from 960 to 1 ,21 5 Mc. It was designed primarily for ground-based 
transmitters used for air-navigation aids such as Tacan. The peak power available 
from the tube is 25 kw, which is only a modest power for most radar applications. 
Thirty watts of drive power is required, and the efficiency is better than 30 per cent. A 
control grid generates a Gaussian-shaped pulse to minimize interference between 
adjacent navigation channels. The grid requires a total voltage swing of only 3.2 per 
cent of the beam voltage to get full rated power of 25 kw. The duty cycle is 0.025, and 
the pulse repetition frequency used in the air-navigation-aid application is 7,000 cps. 




6 8 10 
Frequency, 



100 



Fig. 6.18. Average power of pulsed-klystron amplifiers with space-charge focusing as a function of 
frequency. {Personal communication from C. M. Veronda of the Sperry Gyroscope Company?) 

A plot of the maximum average power output from space-charge-focused klystron 
amplifiers as a function of frequency is shown in Fig. 6.18. Peak powers up to about 
500 kw are permissible, and paralleling of tubes to achieve greater power is compara- 
tively simple. The power output of the SAL-89 klystron described above falls short of 
that indicated by Fig. 6.18 since it is limited in power by the output connector and not 
by the focusing. A companion tube, the SAL-219, has average power outputs falling 
on the curve. 

The klystron amplifier may be used for CW as well as pulse applications. The 
electromagnetically focused VA-849 JV-band CW klystron amplifier delivers 20 kw of 
CW power with low incidental noise in the frequency range from 7.125 to 8.5 Gc. It 
has a gain of 50 db with a bandwidth of 30 Mc and is tunable over 60 Mc. A pure C W 
signal with little extraneous noise is especially important in long-range C W applications . 
The AM and FM noise in the VA-823 series of klystrons (5 kw of CW power at JVband) 
is 100 db below the carrier in any 1-kc channel more than 1 kc removed from the carrier. 

The Monofier is a form of klystron with good frequency stability, low noise, and 
comparatively good efficiency. It employs a single electron beam and contains two 
cavities separated by a drift space. The first cavity encountered by the electron beam 



224 Introduction to Radar Systems 



[Sec. 6.3 



is a self-excited oscillator which velocity-modulates the beam. As the beam traverses 
the drift space, the velocity modulation is converted to density modulation. The RF 
power in the density-modulated beam is extracted on passing through the second, or 
catcher, cavity. Thus the Monofier serves the function of two tubes. Electro- 
statically focused CW Monofiers at X band are capable of 1 or 2 kw of power with 
efficiencies of 20 to 25 per cent. The Monofier may also be designed to operate 
pulsed. Possible areas of application include compact CW and pulse-doppler radar 
systems. 

Bandwidth of Multicavity Klystrons. i5 ~~ &1 Almost all high-power klystron amplifiers 
employ more than two cavities. The advantages of the additional cavities are an 
increase in gain, greater efficiency, and the capability of obtaining wider bandwidths. 
In the UHF band, the RF conversion efficiency of a two-cavity klystron is of the order 
of 20 to 30 per cent, with gains of the order of 20 db. The efficiency of a three-cavity 
amplifier might vary from 35 to 45 per cent, with 30- to 40-db gain. The efficiency 

Table 6.2. Comparison of Computed Gain and Bandwidth of Multicavity Klystrons 

at 700 Met 





Gain, db 


Bandwidth, Mc 


Number of cavities 


Synchronous 
tuning 


Stagger 
tuning 


Synchronous 
tuning 


Stagger 
tuning 


2 
3 
4 
Two two-cavity tubes in cascade 


20 
45 
70 
40 


30 
40 


4 
2 
1 
2.5 


6.5 
9 







t Dain. 64 

does not increase significantly as more cavities are added, but the gain is increased and 
wider bandwidths may be achieved. The gain of a four-cavity klystron can be 60 db or 
greater. 

The broadbanding of a multicavity klystron may be accomplished in a manner 
somewhat analogous to the methods used for broadbanding multistage IF amplifiers. 
One of the more common techniques is to stagger-tune the frequencies of the various 
cavity stages. Stagger tuning of a klystron is not strictly analogous to stagger tuning a 
conventional IF amplifier, because interactions between nonadjacent cavities cause 
the tuning of one cavity to affect the tuning of the others. 45 Consequently, the broad- 
banding of klystrons is somewhat empirical in practice, although there has been some 
theoretical work to serve as a guide. The adjustment of the cavity frequencies for 
broad bandwidth in a multicavity stagger-tuned klystron is a complex procedure and is 
probably better performed at the factory than in the field. 

From the theory of electron bunching in a multicavity klystron, the gain and band- 
width have been calculated by Kreuchen et al. 46 for klystrons with two, three, and four 
cavities, using numerical parameters considered typical of a klystron operating at 
700 Mc. Some of the results, as reported by Dain, 54 are presented in Table 6.2. The 
gain-bandwidth product increases significantly with additional cavities. The entries 
in the table show that the gain and the bandwidth of a single four-cavity klystron are 
considerably better than those of a pair of two-cavity klystrons in cascade. 

It has been reported that the half-power bandwidth of the S-band VA-87 klystron 
amplifier can be increased from its synchronously tuned bandwidth of 27 Mc to a value 
of 77 Mc by stagger tuning. 47 This represents a 2.8 per cent bandwidth. The 
increase in bandwidth is accompanied by a decrease in gain from about 57 db with 
synchronous tuning to about 44 db with stagger tuning. A special modification of the 



Sec. 6.4] Radar Transmitters 225 

VA-87 using a six-cavity driver section followed by an output section consisting of a 
double-tuned circuit with an inner cavity identical with that of the VA-87 results in a half- 
power bandwidth of 4. 8 per cent, or 1 44 Mc. (In the double-tuned cavity arrangement 
the usual output cavity is coupled not only to the load but to a secondary cavity of 
adjustable loss and frequency. 52 ) The gain of the tube was in excess of 40 db. The 
commercial version of this tube is the VA-839. It is capable of 5 Mw peak and 10 kw 
average power at an efficiency of 40 per cent. 

In practice, stagger tuning enables the bandwidth of the multicavity klystron amplifier 
to be increased from a synchronously tuned bandwidth of \ to £ per cent to values the 
order of 5 per cent or more, with a reduction in the gain. 

Bandwidths of multicavity klystrons may be as large as 1 to 1 2 per cent or greater. 
This is comparable with that available with high-power traveling-wave tubes. 



51.53 



-47.54-59 



6.4. Traveling-wave-tube Amplifier 4 

The wide bandwidth of the traveling- wave amplifier is its chief attribute of interest to 
the radar engineer. A wide bandwidth is necessary in applications where good range 



Cothode- 



/ Gun J A ttenuatio n Collector- 

/ anode 4 #mm >. Elector- 



Heater-* 






. ii I H.n/ . , ir 

Electron S 1*1 (interaction region) I I I 

beam I ' 

RF RF 

input output 



Fig. 6.19. Diagrammatic representation of the traveling-wave tube. 

resolution is required (Sec. 10.8) or where it is desired to rapidly tune the radar within a 
wide frequency band to avoid deliberate jamming or mutual interference with nearby 
radars. Bandwidths of the order of 10 to 20 per cent are possible with the traveling- 
wave amplifier at the power levels required for long-range radar applications. 

Description. A diagrammatic representation of a traveling-wave tube is shown in 
Fig. 6.19. The electron optics of the traveling- wave tube are similar in many respects 
to those of the klystron. Both employ the principle of velocity modulation, the 
klystron in the form of standing waves, the traveling- wave tube in the form of traveling 
waves. Electrons emitted by the cathode of the traveling-wave tube are focused into a 
beam and pass through the RF interaction region. After delivering their d-c energy to 
the RF field, the electrons are removed by the collector electrode. The RF signal to be 
amplified enters via the input coupler and propagates along the periodic structure. 
The periodic structure is shown as a helix in Fig. 6.19, a popular form for low-power, 
large-bandwidth tubes. The velocity of propagation of electromagnetic energy is 
slowed down by the helix and is nearly equal to the velocity of the electron beam . For 
this reason, it is sometimes called a slow- wave structure, or a periodic delay line. I n the 
helical line the wave travels along the wire with about the speed of light but the velocity 
of propagation in the direction of the beam is somewhat less. For example, if the wire 
is 13 times as long as the axial length of the helix, the wave will travel along the beam 
with one-thirteenth the speed of light, and the electrons will be in synchronism with 
the wave if they are accelerated by about 1,500 volts. The synchronism between the 
electromagnetic wave and the electrons results in a cumulative interaction which trans- 
fers energy from the d-c beam to the RF wave, causing the RF wave to be amplified. 

The RF signal, when applied to the input coupler of the traveling- wave tube, velocity- 
modulates the electron beam just as in the klystron. The velocity modulation is 
transformed into density modulation (bunches) after traveling a short distance down 



226 Introduction to Radar Systems [Sec. 6.4 

the tube. When the electrons are bunched, the concentration of space charge produces 
a repelling effect and the beam becomes debunched ; that is, density modulation is 
converted back to velocity modulation. As the electrons travel farther along the tube, 
the velocity-modulated electron beam is again converted to density modulation, and 
the process is repeated. Thus standing waves of space charge exist along the beam. 
These standing waves may be described as the beating of two space-charge waves 
traveling along the beam with different phase velocities. One of the waves has a phase 
velocity smaller than the beam velocity, while the other wave has a phase velocity larger 
than that of the beam. The slower space-charge wave, when coupled to the electro- 
magnetic wave, is used in the traveling-wave amplifier. The faster space-charge wave 
is used in electron accelerators. 

The periodic structure usually associated with traveling-wave tubes is the helix. The 
helix is well suited to low-power, broadband applications but cannot be used at high- 
power levels (greater than approximately 10 kw) since it does not dissipate heat effec- 
tively. Other types of slow-wave structures must be used for high-power levels. Un- 
fortunately, the type of periodic structures suitable for high powers does not have as 
wide a bandwidth as some of the lower-power structures. 

The high-power traveling-wave tube is very similar to the klystron. In some 
respects, the traveling-wave tube might be considered as a limiting case of the multi- 
cavity klystron. One of the major differences between the usual klystron and the 
traveling-wave tube is that feedback along the periodic structure is possible in the 
traveling-wave tube whereas the back coupling of RF energy in the klystron is negligible. 
If sufficient energy were fed back to the input, the traveling- wave tube would oscillate. 
Feedback energy might arise in the traveling- wave tube from the reflection of a portion 
of the forward wave at the output coupler. Because of feedback the traveling-wave 
tube is inherently a less stable device than the klystron. The feedback energy must be 
eliminated if the traveling- wave amplifier is to function satisfactorily. Energy traveling 
in the backward direction may be reduced to an insignificant level in most tubes by the 
insertion of attenuation in the periodic structure. The attenuation may be distributed, 
or it may be lumped, but it is usually found within the middle third of the tube. It must 
be carefully matched to the periodic circuit. The attenuator must be designed so that 
the reflected wave from the output coupler is attenuated much more than the input wave 
is amplified. The introduction of attenuation reduces the efficiency and power output, 
but it, or some substitute, is necessary for proper operation. The necessity for an 
attenuator capable of handling large average powers is one of the major restrictions on 
the output power of a traveling-wave tube not found in the klystron. 

An axial magnetic field (not shown in Fig. 6.19) confines the beam and prevents it 
from dispersing. The electromagnets required for focusing might be quite large. In 
some traveling- wave tubes a considerable reduction in weight is possible by using 
permanent magnets periodically spaced along the tube, but this technique is probably 
better suited to low-power than to high-power tubes. 

Power and Bandwidth. In principle, the traveling-wave tube should be capable of as 
large a power output as the klystron. The cathode, RF interaction region, and the 
collector are all separate and can be designed to perform their required functions 
independently of the others. In addition, the over-all size of the traveling-wave tube 
is usually not small, enabling the structure to dissipate considerable heat. In practice, 
however, it is found that there are limitations to very high power output. 

One of these limitations is the problem of obtaining a feedback attenuator which can 
dissipate the necessary power in a small space and at low voltage-standing-wave ratio. 
Another major limitation is the periodic structure. It seems that those periodic 
circuits best suited for broad bandwidth have the lowest power-transfer and heat- 
transfer dissipation capabilities. Thus, if the traveling-wave tube is to achieve power 



Radar Transmitters 



227 



Sec. 6.5] 

levels comparable with other tube types, a sacrifice in bandwidth must be made. If the 
bandwidth is too small, however, there is little advantage to be gained with a traveling- 
wave tube as compared with multicavity klystrons. 

Traveling-wave tubes have been built which operate at the megawatt level with the 
order of 10 per cent bandwidth at 5 band. 57 Although a 10 per cent bandwidth may 
not be as spectacular as the octave bandwidths possible with low- or medium-power 
traveling-wave tubes, it is nevertheless a significant bandwidth for most radar applica- 
tions. The gain and efficiency of a high-power, broadband traveling-wave tube are 
usually not as good as those of the klystron. A reduction in gain accompanies a large 
bandwidth, just as with the klystron. The saturation gain of the S-band tube referred 
to above was about 20 db, and the efficiency was about 14 per cent. 

Example of Traveling-wave Tube for Radar. The Varian traveling-wave-tube pulsed 
amplifier known as the VA-125 is a commercially available broadband, liquid-cooled 
tube intended to cover the major portion of the S-band radar frequency range. Its 
bandwidth is 300 Mc at a frequency of 3,000 Mc. The peak power output is 2 Mw, and 
the duty cycle is 0.002, with a 2-^sec pulse width. The power gain is 33 db. 

The VA-125 is similar in many respects to the VA-87 klystron amplifier. They 
deliver about the same peak power and can be used interchangeably except that the 
VA-125 traveling- wave tube requires additional input power because of its lower gain. 

6.5. Amplitron and Stabilitron 60 " 6 

Amplitron. The Amplitron is a crossed-field amplifier characterized by high peak 
and average power output, broad bandwidth, exceptionally high efficiency, but low 



Space-charge hub 



Space chargi 
spoke 




Conducting vanes 
ties 



Phase velocity 



Catho 



Conducting 
straps 



roup velocity 



Anode 



Input pla 



Fig. 6.20. Basic structure of the Amplitron. A magnetic field is applied parallel to the axis of the 
tube. {Courtesy Raytheon Company.) 

gain. Amplitrons at L band, for example, are capable of 5 to 10 Mw of peak power at 
duty factors of approximately 0.001, with better than 85 per cent conversion efficiency 
over a bandwidth of more than 10 per cent. Gains are of the order of 10 db. 

The physical structure of the magnetron oscillator and the Amplitron are similar, but 
their characteristics are quite different. The chief physical difference between the two 
is that the Amplitron uses two external couplings (an input and an output) and the 
magnetron has but one. 

A drawing of the workings of an Amplitron is shown in Fig. 6.20. The electrons 
originate from a continuously coated cathode coaxial to the RF circuit. No external 
heater power is usually required for starting the Amplitron or during operation. The 



228 Introduction to Radar Systems [Sec. 6.5 

anode consists of a series of vanes. It acts as both a slow- wave RF circuit with which 
the electrons interact and as an electrode for the collection of electrons. 

The Amplitron is a crossed-field device in that the electron beam is perpendicular to 
both the electric and magnetic fields, just as in the magnetron. Its operation is similar 
in some respects to the traveling-wave-tube amplifier since amplification occurs because 
of an interaction between a traveling electromagnetic wave and a rotating space-charge 
wave. The space-charge waves in the Amplitron are formed by the interaction 
between the electron beam and the crossed electric and magnetic fields. In the traveling- 
wave-tube amplifier the space-charge wave interacts with a forward wave, that is, a wave 
whose phase velocity is in the same direction as the power flow. It is also possible for 




Fig. 6.21. QK 622 5-band Amplitron. (Courtesy Raytheon Company?) 

the RF periodic structure to support backward waves, or waves whose phase velocity is 
opposite to the power flow. A traveling-wave tube in which the space-charge wave is 
coupled to a backward wave is known as a backward-wave amplifier. Space-charge 
waves in a crossed-field-magnetron-type device can couple with either a forward or a 
backward wave. The crossed-field device called the magnetron amplifier uses the 
forward wave and can attain efficiencies of about 50 per cent, bandwidths of 1 5 per cent, 
gains of 15 db, and output power of several megawatts peak. 54 . 63 . 66 - 69 The crossed- 
field device which couples the backward wave to the space-charge wave (Amplitron) 
has a higher rate of gain than the forward-wave device (magnetron amplifier) and for 
the same length will be more efficient. 

Figure 6.20 shows that the electron beam reenters the interaction space just as in the 
magnetron oscillator. However, unlike that of the magnetron, the RF circuit is not 
reentrant. The RF output and the RF input are decoupled. In this sense, the RF 
circuit of the Amplitron is related more to that of the traveling-wave tube than to the 
magnetron. The nonreentrant circuit of the Amplitron permits a broader bandwidth 
than the reentrant circuit of the conventional magnetron oscillator. 

The Amplitron behaves as a saturated amplifier rather than as a linear amplifier. 
The characteristic of a saturated amplifier is that the magnitude of the RF output is 
independent of the RF input, but dependent on the d-c input. Although a saturated 



Radar Transmitters 



229 



Sec. 6.5] 

amplifier cannot be used in some applications, such as, for example, AM voice communi- 
cations, there are but few restrictions on its use as a pulsed amplifier for most radar 
applications. A saturated amplifier is compatible with frequency modulation, and it 
may be used with radars designed with pulse compression. 

The Raytheon type QK 622 pulse Amplitron is shown in Fig. 6.2 1. 64 It produces a 
peak power of 3 Mw when the RF drive power applied to its input is no less than 550 kw. 
The gain is 7.5 db. Its duty cycle is 0.005. When used with a line-type modulator, it 
will cover the frequency band from 2,900 to 3,100 Mc without mechanical or electrical 
adj ustment. Efficiencies greater than 70 per cent are observed over the entire frequency 
band. They approach or even exceed 80 per cent at some frequencies. At reduced 



10,000 



1,000 



100 




10 100 1,000 

Peak RF power input, kw 



10,000 



Fig. 6.22. Plot of the RF power output as a function of the RF power input for the Raytheon QK 520 
L-band Amplitron. Contours show constant modulator input. (From Brown,™ reprinted, by 
permission, from the Apr. 29, 1960, issue of Electronics, a McGraw-Hill publication, copyright, 1960.) 

power output, the gain is increased. Eleven decibels is obtained when the peak power 
is 700 kw. The weight of the completely packaged QK 622 as shown in Fig. 6.21 is 
1251b. 

A plot of the RF power output as a function of the RF and d-c modulator input power 
is shown in Fig. 6.22 for the Raytheon QK 520 L-band Amplitron. 66 For constant d-c 
input power, the RF output power is relatively independent oftheRF input power, except 
when the RF input becomes comparable with the RF output. This departure from 
saturated amplifier behavior results from a slight increase in efficiency with large RF 
input power and because the input power reappears unattenuated at the output and 
adds to the RF power generated by the Amplitron itself. If, at a given level of d-c 
power, the RF input is reduced below a certain level, the device ceases to act as an 
amplifier. In this region (shown shaded in Fig. 6.22), the RF output is noisy, poorly 
defined, and at some other frequency than the input signal. The transition region 
between the area in which the input does not control RF output and the area in 
which performance is satisfactory is well defined and of negligible width. 

The conversion efficiency of an Amplitron is defined as follows : 



Efficiency 



RF power output — RF power input 
modulator power input to Amplitron 



(6.4) 



230 Introduction to Radar Systems [Sec. 6.5 

This is a conservative definition since the RF input power is not lost but appears as part 
of the output. In a low-gain amplifier the input power which appears at the output 
may be a sizable fraction of the total. The effective over-all efficiency of a chain of 
Amplitrons therefore can remain high. 

The high efficiency permits operation at considerably greater power levels than other 
tube types with similar heat-dissipation capabilities but of lower efficiencies. Assume, 
for example, that a particular tube structure can safely dissipate 10 kw of heat and that 
this is the only limitation on the total power the tube can generate. If the efficiency of 
the tube were 20 per cent, the useful power output would be 2.5 kw and the power 
dissipated 10 kw. On the other hand, if the efficiency were 80 per cent, the tube could 
deliver 40 kw while dissipating 10 kw. An increase in efficiency by a factor of 4 from 
20 to 80 per cent results in a 1 6-fold increase in the amount of output power delivered to 
a load. The high efficiency of the Amplitron is one of the major reasons for its ability 
to generate large powers with structures of reasonable size. (The advantages to be 
gained from high efficiency apply to any type of device and are not proprietary to the 
Amplitron alone.) The Amplitron has the advantage that it is one of the most efficient 
of the high-power microwave amplifiers. 

The phase shift through the Amplitron caused by a change in the d-c current applied 
to the device is called phase pushing, by analogy with the term frequency pushing, which 
describes a similar phenomenon in oscillators where the frequency is changed or pushed 
as the current is changed. Phase pushing in an Amplitron is usually quite small 
compared with other microwave amplifiers, being of the order of a fraction of a degree 
per ampere. Low phase pushing is important in radar applications where zero or 
negligible phase shift must be maintained between input and output. Such would be 
the case when several power tubes are operated in parallel or when individual trans- 
mitters feed individual elements of a phased array antenna. The phase shift varies less 
than 0.5° for a 1 per cent variation in anode current with Amplitrons like the QK 622. 
The Amplitron operates with low RF voltages and possesses good stability. The 
percentage of missing pulses in the QK 622 is less than 0.05 per cent. 

The quality of the output spectrum from the Amplitron is but little affected by changes 
in load conditions. It is reported 61 that the output spectrum of a particular Z.-band 
tube remains unperturbed regardless of phase position of output mismatch and VSWR 
up to a value of 2.5. 

The Amplitron acts as a passive transmission line when the high voltage is removed. 
Its insertion loss is low, typically 0.2 to 1 .0 db. Therefore an RF signal traveling in the 
reverse direction from the output to the input suffers little attenuation. This differs 
from other amplifiers in which the reversed signal is highly attenuated. The low 
insertion loss makes it possible to pass the received echo signal back through the 
Amplitron before entering the duplexer. Duplexing may therefore be accomplished 
at a lower power level than if it had to be placed at the output of the tube. However, 
the low attenuation in the backward direction requires that a high-power circulator or 
some other isolation device be used between Amplitron and driver to prevent the 
reflected power from interfering with the driver portion of the transmitter or from 
building up into oscillation. Isolation is also needed between Amplitrons when they 
operate in cascade. 

Amplitron voltages are lower than those of the klystron or the traveling-wave tube 
and are comparable with those of the magnetron. A magnetic field is required just 
as with the magnetron. Permanent magnets are usually used. The magnitude of the 
magnetic field represents a compromise between magnet weight and the higher efficiency 
which can be obtained with large magnets. 

An unusual feature of the Amplitron is its ability to operate without a cathode 
heater. The tube starts without a cathode warmup period whenever RF drive power 



Sec. 6.5] 



Radar Transmitters 231 



is present prior to application of the modulating pulse. The absence of a heater 
results in longer tube life. The life of the QK 622 is claimed to be in excess of 
l,000hr. 64 

Because of its relatively low gain but high power and high efficiency, one application 
of the Amplitron has been as a booster tube to increase the power output of existing 
radar equipments. It is simply added to the output of the existing radar to give an 
order-of-magnitude increase in radiated power. No tuning of the tube is necessary 
because of its broad bandwidth, and the duplexer can often be used without change on 
the input side of the Amplitron. It is usually necessary, however, to employ a ferrite 
isolation device on the input side to prevent unwanted oscillations from building up 
because of the reflections from mismatches at the output and input. 

The gain of an Amplitron can be increased at the expense of the bandwidth by the use 
of positive feedback produced by inserting mismatches in the input and output trans- 
mission lines. These are inserted so that the RF energy reflected from the mismatch i n 
the output line will be returned to the mismatch in the input line and be again reflected 
in such phase as to add with the input energy. 70 Gains of the order of 30 db can be 
obtained with bandwidths of the order of \ per cent. Mechanical tuning over a 1 per 
cent range is possible. 




Amplitron 




Partiol 
reflection 
(mismatch) 




Useful 
load 


(Plotinotron) 







Fio. 6.23. Block diagram of Stabilitron oscillator consisting of an Amplitron with a high-Q cavity 
attached to the input and a broadband mismatch reflection on the output. 

The Amplitron is capable, in principle, of extremely large power. A tube the size of 
the QK 622 (average power of 15 kw), with an anode cooled with high-velocity liquid, 
should be capable of delivering a useful RF average output power of more than 100 kw 
at S band. 71 

Stabilitron. The Amplitron can be made to operate as a highly stabilized oscillator 
by the addition of RF feedback and the application of a stabilizing cavity (Fig. 6.23). A 
mismatch is connected between the output of the tube and the load. A high-g, 
narrowband tunable cavity is connected to the tube input. A portion of the power 
output from the Amplitron is reflected by the mismatch and travels back through the 
tube in the direction of the input with little or no attenuation. The high- Q cavity 
absorbs that energy not at the resonant frequency of the cavity. Energy which is at 
the resonant frequency is re-reflected and passes through the device in the forward 
direction with amplification. Steady oscillations will occur if the total phase shift from 
the output reflection to the cavity reflection and return is an integral multiple of 2tt 
radians and if the gain around this loop is greater than unity. The latter requires that 
the product of the output reflection coefficient, times the cavity reflection coefficient, 
times the attenuation in the backward direction, times the gain in the forward direction 
be greater than 1. The frequency of oscillation is also determined by the resonant 
frequency of the cavity. The purpose of the phase shifter shown in the diagram of 
Fig. 6.23 is to adjust the phase of the feedback loop to be compatible with the resonant 
frequency of the cavity. It is not necessary in fixed tuned devices or where the tuning 
range is small. 

The high Q of the cavity resonator acts to stabilize the frequency of oscillation. The 
phase shift vs. frequency characteristic of the stabilizing cavity has a larger slope than 
any other part of the circuit; consequently, a slight change in frequency permits the 
cavity to correct for substantial phase shift which might be introduced by such factors 



232 Introduction to Radar Systems [Sec. 6.5 

as a change in antenna impedance or frequency pushing. The Amplitron, when used 
in the manner described above to generate oscillations, is called a Stabilitron. 

The frequency stability of the Stabilitron is from 5 to 100 times as good as that of the 
magnetron, depending upon the type of frequency stability considered, for example, 
whether the frequency pulling figure or the frequency drift due to temperature change is 
being compared. A high-g cavity can also be used in conjunction with a magnetron 
oscillator as it is in the Stabilitron, to further improve its frequency stability. However, 
in the magnetron oscillator, the stabilizing cavity must be inserted in the output rather 
than the input. Therefore, for a given degree of frequency stabilization, a much higher 
circuit efficiency can be obtained with the Stabilitron than with the magnetron since the 
stabilizing cavity placed at the input to the Stabilitron absorbs less power than a cavity 
at the output. 

The pulling figure of the Stabilitron, which is a measure of the change in frequency 
produced by a change in the external load, is about 5 to 20 times less than normally 



Table 6.3. Comparison of Typical Operating Values 
of Radar Oscillators 



Characteristic 


Magnetron 
5J26 


Stabilitron 
QK 630-629 


Pulling figure, Mc 


2-2.5 

50-100 

46 

28 

42 

550 

550 

1,220-1,350 

1,400 


4-0 6 


Pushing figure, kc/amp 


1-4 


Peak operating current, amp 

Operating potential, kv 


40 
36 


Typical efficiency, % 


52 


Peak output power, kw 


650 


Average power output, watts 

Tuning range, Mc 


1,560 
1,260-1,350 
1,150 


Operating magnetic field, gauss 



associated with the magnetron. A consequence of the lower pulling figure is that the 
Stabilitron is less subject to long-line effect [Eq. (6. 1)] than is the magnetron. Therefore 
the Stabilitron can be operated into transmission lines several times longer than is 
possible with the magnetron before frequency jumping, because of the long-line effect, 
causes trouble. 

Phase pushing of the Amplitron is manifested as frequency pushing— change in 
frequency with change in anode current— in the Stabilitron. Its effect is minimized, 
however, by the presence of the stabilizing cavity. An improvement in the dynamic 
pushing figure of from 10 to 50 is possible, depending upon the particular type of 
magnetron used for comparison. 

The efficiency of the Stabilitron is quite good. It might vary from 45 to 60 per cent 
across the tuning range. The broadband properties of the Amplitron are also reflected 
in the Stabilitron. The latter may be tuned over a 5 to 10 per cent frequency band by 
changing the resonant frequency of the stabilizing cavity and the phase shift in the line 
connecting cavity and tube. 

A comparison of typical operating values of a radar magnetron oscillator and a 
Stabilitron is shown in Table 6.3. 

Platinotron. This is the name given to the basic crossed-field structure used for both 
the Amplitron and the Stabilitron. Its name is derived from the Greek word platys, 
which has the connotation of broad, flat, and, less frequently, to amplify. Thus 
Platinotron is meant to apply to an amplifier with broadband properties. Physically, 
the Amplitron and the Platinotron cannot be distinguished from one another. 



Sec. 6.6] Radar Transmitters 233 

6.6. Grid-controlled Tubest 

The early radars developed in this country and abroad during the 1930s used con- 
ventional grid-controlled tubes since there existed no other source of large RF power. 
This limited the development of the early radars to the VHF and the lower UHF bands. 
The Navy's first prototype radar, the XAF, used a 100T Eitel-McCullough triode tube 
operating at a frequency of 200 Mc. 72 Six tubes were operated in a ring circuit to 
achieve greater power. Each tube had a plate dissipation of 100 watts. These tubes 
were also used in the Army's first fire-control radar, the SCR-268. The Army's 
long-range search radar, the SCR-270, used a Westinghouse tube, the VT-122, and 
operated at 1 10 Mc. Both tubes were of relatively low power compared with postwar 
grid-controlled tubes. 

The grid-controlled tube has been employed in many applications at the lower radar 
frequencies (VHF and UHF). When the discovery of the cavity magnetron led to the 
successful development of microwave radar early in World War II, interest in lower- 
frequency radars waned. During the postwar years, the needs for higher average- 
power radar equipments and better MTI performance were two of the factors which 
renewed interest in the lower UHF and VHF radar bands. Considerable improvement 
was made after the war in the development of grid-controlled tubes for operation at 
increasingly higher frequencies. The upward frequency scaling of grid-controlled 
tubes was spurred by applications in particle accelerators, scatter communications, 
UHF-TV, and radar. Meanwhile, equally significant developments were being made 
in the postwar development of new tube types such as the klystron, the traveling-wave 
tube, and the Amplitron. During the late 1950s, these newer devices were scaled 
downward in frequency and were highly competitive with grid-controlled tubes in the 
400 to 1,000-Mc region of the spectrum. However, the grid-controlled tube was 
capable of more average power per "bottle" than any other tube type at frequencies 
below 1 ,000 Mc. Although the grid-controlled tube can theoretically be scaled upward 
into the microwave region of the spectrum, the newer electronic generators have already 
demonstrated their microwave performance capabilities. 

The type of grid-controlled tube considered here is the conventional triode or tetrode 
configuration operated in a vacuum. It is the direct descendant of the DeForest 
Audion. A detailed description of the operating principles of these tubes may be found 
in any classical text on vacuum tubes, such as that by Spangenberg. 73 

The potential applied to the control grid of the tube acts as a gate, or valve, to control 
the number of electrons traveling to the plate. The variation of potential applied to 
the grid is imparted to the current traveling to the plate. The process by which the 
electron stream is modulated in a grid-controlled tube is called density modulation. 

Limitations at High Frequency. Grid-controlled tubes are capable of megawatts of 
CW power at the lower communication frequencies. Respectable power outputs have 
been obtained at frequencies as high as S band. Some of the factors limiting the high- 
frequency performance of power tubes as the frequency is increased are (1) increased 
circuit reactances, (2) RF losses in dielectrics, (3) transit-time effects, (4) reduced average 
power-handling capability due to smaller-size structures, and (5) reduced peak power 
capability. All these factors will be discussed for the grid-controlled tube, but it should 
be kept in mind that they are pertinent in the higher-frequency performance of all 
classes of tubes. 

In any tube there will always be unavoidable capacitance and inductance. The 
capacitance in the grid-controlled tubes is primarily that of the grids, the cathode, 
and the plate electrodes. The inductance is caused by the connections made to the 

t Much of the material in this section was made possible from information kindly supplied by 
Merle V. Hoover of RCA Tube Division, for which the author wishes to express his appreciation. 



234 Introduction to Radar Systems [Sec. 6.6 

electrodes. Reactances may be minimized, but never entirely eliminated. Small-size 
electrodes spaced far apart result in small interelectrode capacity. However, the 
minimum size of electrodes is determined in large part by the power dissipation required 
of the structure. Also, the electrode spacing cannot be made too large without 
encountering increased transit-time effects. The reactive components act to shunt the 
input to the tube and short-circuit the tube as the frequency is raised. This causes a 
decrease in the power. Spangenberg 73 shows that the cathode lead inductance reflects 
back to the input as a shunt resistance whose value is inversely proportional to the 
square of the frequency. The reactance of the input capacity (grid-cathode capacity in 
a grounded-cathode tube) also shunts the input and is inversely proportional to the 
frequency. The inductance of the leads can be minimized by using coaxial transmission 
lines or waveguide and by designing the resonant circuits the same as microwave 
cavities. Most high-power tubes use microwave-circuit techniques. Some are 
designed with the resonant cavities entirely within the vacuum envelope. 

Another factor contributing to the degradation of output power as the frequency is 
increased is the RF loss. The resistance of the conducting parts of the tube increases 
with increasing frequency because of the skin effect. The skin-effect resistance, and 
hence the PR power loss, is proportional to the square root of the frequency. Losses 
may also occur by radiation of electromagnetic energy from the tube elements or 
lead-ins. Radiation loss is proportional to the square of the frequency. Both the 
skin-effect loss and the radiation loss can be minimized by operating the tube inside 
resonant-cavity structures, a practice almost always employed in modern high-power 
tubes. 

An important source of RF loss is the heating of the dielectric materials used in the 
construction of the tube for insulating supports or for the envelope which encloses the 
vacuum. If the dielectric is in the RF field, the field can excite molecular movements 
which result in heating. Dielectric-heating losses are directly proportional to the 
frequency. They may be minimized by placing insulators outside the RF field or at 
least in regions of weak fields. However, it is not always possible to do so. When 
dielectrics must be used in high-power-tube construction, it is important to use as low a 
loss dielectric as possible. For this reason most modern tubes use low-loss ceramic 
instead of glass. It is claimed 74 that replacing the glass envelope of the 2C39A (a 
relatively low power triode) with a high-alumina (A1 2 3 ) ceramic envelope results in an 
increase in power of 10 per cent at a frequency of 2,500 Mc. Tubes with ceramic 
envelopes are mechanically stronger than tubes with glass envelopes and can withstand 
higher temperatures, both in operation and during bake-out. Maximum operating 
temperatures can usually be increased 50 to 75°C over an equivalent glass insulated 
tube. 75 Ceramic tubes are more reliable than those of glass and are also easier to 
adapt to automatic production methods. 

The finite time required for an electron to transit from cathode to plate places a limit 
on the upper usable frequency. 76 - 77 At low frequencies the time taken by an electron 
in traveling from the cathode to the plate can be considered to be instantaneous since 
the transit time is short compared with the period of RF oscillation. However, if the 
frequency is sufficiently high, the time taken by an electron to transit the interelectrode 
distance will be comparable with the RF period and the transit time can no longer be 
considered zero. For example, the transit time of an electron traveling from the 
cathode to the plate in a planar diode under d-c conditions with a space-charge-limited 
current is 54 - 78 

T=6.7xlO- 10 Q (6.5) 

where d ■= electrode spacing, cm 

J = current density, amp/cm 2 



Sec. 6.6] Radar Transmitters 235 

For a triode or a tetrode the distance d is the spacing between the cathode and the 
effective plane of the control grid. For a spacing of 0.05 cm and a cathode current 
density of 1 amp/cm 2 , the transit time is 2.5 X 10 -10 sec. This may seem rather short, 
but it represents about one-quarter of a cycle at a frequency of 900 Mc. The transit 
time is sometimes measured by the transit angle, which is the product of angular 
frequency and the time taken by an electron to traverse the interelectrode space. In the 
above example the transit angle would be 7r/2 radians. 

When the transit time becomes an appreciable fraction of the RF period, a shift occurs 
in the phase between the plate current and the grid voltage. 79 The gain, efficiency, and 
power output are reduced. When the transit time is relatively large, the density- 
modulated electrons are debunched because the transit time of electrons that leave the 
cathode at one moment of the cycle will be different from those departing at another 
moment. Some of the electrons will fail to pass the grid and will be turned back to the 
cathode. If enough electrons are turned back, the temperature of the cathode will 
increase. Cathode back heating can be partially compensated by adjusting the heating 
power applied to the filament, as long as the back heating is small. 

The transit time in the grid-cathode region may be minimized by making the grid- 
cathode spacing as small as possible and operating with a high grid voltage. The 
higher the voltage, the greater the acceleration of the electron and the less the time taken 
in traversing the space. Also, the higher the voltage, the greater will be the current 
density emitted. The minimum spacing between the cathode and the grid is usually 
determined by mechanical design considerations and by the amount of heat from the 
cathode that the grid can safely dissipate. A close spacing requires good fabrication 
technique and careful mechanical design if a grid structure is to be maintained only 
fractions of a millimeter away from a cathode surface operating at high temperature. 

In the trade between cathode current density and electrode spacing as given by Eq. 
(6.5), it is often desirable to increase the current density to avoid making the electrode 
spacing too small. 54 However, the larger the cathode current density, the less will be 
the life of the cathode. 80 

The spacing between grid and plate need not be as small as the grid-cathode spacing 
since the electrons do not start from rest as when they leave the cathode. The minimum 
spacing and the maximum voltage which can be used will be limited by the electrode 
dissipation capabilities. In addition, the smaller the spacing between the grid and the 
plate in a triode, the less will be the bandwidth. 54 Thus the choice of the grid-plate 
spacing represents a compromise between high gain and efficiency, on the one hand, and 
wide bandwidth, on the other. 

It has been mentioned that the transit time can be reduced by the use of high voltage. 
High voltage leads to increased current and power because it is, in general, not possible 
to increase the shunt impedance of the resonant circuit to any great extent without 
reducing the circuit efficiency and the bandwidth. Therefore, from this point of view, 
it is concluded that it should be easier to build high-power tubes rather than low-power 
tubes at the high frequencies if the heat generated can be safely dissipated and if the 
cathode-emission limits are not reached. 81 

To obtain large average power output, the tube must be capable of dissipating the 
heat generated . The heating of the control grid and the screen grid is primarily caused 
by (1) ambient heat radiated from the hot cathode, (2) heat generated by the interception 
of energetic electrons by the grids, and (3) ohmic losses due to the displacement currents 
associated with the RF voltages impressed across the interelectrode capacitances. 
Excessive heat might cause the electrodes to sag or melt. The high-power performance 
might also be limited by the emission of electrons from the overheated grids. The 
thermionically emitted primary electrons can cause damage by being accelerated with 
sufficient energy to bombard other electrodes. Electrons can also be emitted from 



236 Introduction to Radar Systems [Sec. 6.6 

relatively low temperature electrodes by the process of secondary emission. However, 
secondary-emission electrons are not necessarily harmful to tube performance, espe- 
cially in the tetrode. 80 The heating of the control-grid and the screen-grid electrodes 
can be reduced with lower-temperature oxide cathodes and with electron-optical sys- 
tems which minimize the interception of electrons by the grids. Very high power tubes 
use water-cooled grids or other means of conduction cooling to dissipate the heat. 

The plates of high-power tubes must be specifically designed to dissipate the heat 
generated and are frequently water- or air-cooled. Although it must be properly taken 
into account in the design of a tube, plate dissipation is seldom the chief limitation on 
power output, especially in short-pulse application. 80 

The peak power of a tube under pulsed conditions is often limited by the finite 
electron emission available and/or by voltage breakdown. Voltage breakdown may 
occur between the electrodes, across the vacuum envelope insulation, or in the external 
circuitry. The peak power that a tube can withstand before breaking down is usually 
greater in pulse operation than in CW operation. A finite time is required after the 
application of the voltage for a breakdown to occur. Therefore the longer the pulse 
duration, the more likely there will be an arc-over. The amount of current that can be 
drawn from a particular cathode depends upon the material and the amount of life 
desired from the cathode. In general, those cathodes with good emission properties 
such as oxide-coated cathodes are more susceptible to damage by positive-ion bombard- 
ment than the more rugged, but less efficient, cathodes such as pure tungsten or thoriated 
tungsten. 

The size of the tube is proportional to the wavelength. Therefore both the average- 
power and the peak-power capabilities decrease with increasing frequency. If the 
dimensions scale directly as the wavelength, the peak power will vary as the square of 
the wavelength, assuming that the voltage gradient required for breakdown is independ- 
ent of frequency. The surface area will also vary as the square of the frequency, and if 
heat dissipation is proportional to area, the average power varies inversely as the square 
of the frequency. It should be borne in mind that the above is only approximate. 
The variation of average and peak power may be a complicated function of frequency 
in a specific tube design. 

Beam Power Tubes. The beam power tube is a tetrode designed so that the electrons 
move from cathode to anode in dense sheets. 73 This effect is accomplished by aligning 
the windings of the control grid and the screen grid. The high concentration of negative 
charge caused by the dense current sheets between the screen grid and the plate sup- 
presses the flow of secondary electrons from the plate to the grid which occurs in a 
normal tetrode. The effect of the secondary electron flow in the normal tetrode 
construction is to distort the plate-current characteristic curves. Secondary emission 
can distort the characteristics to the point where the tube has the effect of a negative 
resistance. The purpose of adding a suppressor grid to a tetrode, making it a pentode, 
is to suppress the secondaries. The large negative current sheets of the beam power 
tube have the same effect as the pentode's suppressor grid in reducing the secondaries. 
Tubes which use the beam-power electron optical system provide high power, high gain, 
low-feedback effects, and good over-all performance. The beam power tube has 
proved to be quite popular for conventional applications. The 6L6, 807, 829-B, and 
the 4X250 are all examples of beam power tubes. 

Because of its success at the lower frequencies the beam-power-tube configuration 
has also been applied in high-power UHF applications. An example of the design of 
a UHF beam power tube capable of 1 kw of CW power at a frequency of 
1,000 Mc is the RCA-7214. 82 It is capable of delivering 100 kw of peak power at a 
duty factor of 0.01. One of the biggest single-unit beam power tubes is the RCA 
development type A-2581, which is supposed to be capable of delivering 1 Mw peak 



Sec. 6.6] 



Radar Transmitters 237 



Screen 
block 



(RF by-passed 
to filaments 
and cathode 
shell) 




power at a frequency of 500 Mc when operating as a pulse amplifier with a gain of 10 db, 
a 10-^asec pulse width, and a 0.01 duty factor. This is a ceramic tube with an over-all 
length of 6.2 in. and a diameter of 5.5 in.f The single-unit beam power tubes are 
characterized by small size and rugged construction. 

The tubes described above are of medium power. They might be used in moderate- 
capability radars or in high-power array radars where the antenna is made up of a large 
number of individual radiating elements each fed by its own moderate- or small-size 
transmitter. 

Multiple-unit Tube Construction. The type of tube construction consisting of a 
single cathode, one or two grids, and a plate is limited in power capability by the amount 
of heat which a single unit can dissipate. The 
larger the tube, the more heat it can dissipate 
and the greater the power output. It has 
already been mentioned that the size of the 
tube structure is proportional to the wave- 
length, so that the higher the frequency, the 
smaller the tube and the smaller is the power 
that the tube can dissipate. 

At a fixed frequency the unit cannot be made 
larger than some maximum size without en- 
countering difficulties due to the generation of 
higher-order modes in the RF circuitry or to 
increased transit-time effects. One technique 
for increasing the power output is to employ 
in parallel a number of unit electron-optical 
structures arranged in a coaxial, cylindrical 
configuration, all within the same vacuum en- 
velope. The multiplicity of units operating in 
parallel permits the attainment of high power 
from a single "bottle" since the heat to be dis- 
sipated is spread over a relatively large area. 

Figure 6.24a is a cross-sectional sketch of 
two UHF beam-power tetrode units. 80 ' 83 - 84 A 
longitudinal view showing the aligned grid 
wires characteristic of the beam-power con- 
figuration is shown in Fig. 6.246. The spacing 
between the control-grid wires and the fila- 
ments is 0.020 in., as is the spacing between 
the control-grid and the screen-grid wires. 

The tube construction illustrated in this figure is "inverted," since the plate is a cylin- 
drical structure located in the center of the tube, while the cathodes are located on the 
periphery. Forty of these unit tetrodes are used in a cylindrical arrangement in the 
RCA 6806, a commercially available tube designed to give a power output of about 
10 kw in UHF-TV service. Similar construction is employed in the RCA-2041 and 
RCA-6952 tetrodes, pulse versions of the aforementioned RCA-6806 tetrode. The 
6952 is designed primarily for short-pulse operation ; the 2041 , for long-pulse operation. 
They differ from the tubes used in UHF-TV in that the plate-cathode ceramic insulating 
bushing is larger in the pulse version in order to permit the application of higher pulsed 
plate voltage. In short pulse service with a pulse duration of 1 3 /^sec and a duty factor 
of 0.004, the 6952 (Fig. 6.25) is capable of providing a useful peak power output of 2 Mw 
with a power gain of at least 20 db at a frequency of 425 Mc. In long-pulse operation, 

t Data are based on RCA Exhibit No. PTO 920-4, Nov. 19, 1957. 



Cathode 



^X 



.Control grid 
^^Screen 



grid 



Plate 



ib) 



Fig. 6.24. (a) Cross-sectional sketch of two 
unit tetrode elements for beam power UHF 
tube; (b) longitudinal section of unit tet- 
rode element for beam power UHF tube. 
{From Bennett,' 3 IRE Trans.) 



238 Introduction to Radar Systems [Sec. 6.6 

with a pulse duration of 2 msec and a prf of 300 cps (0.06 duty factor), the RCA-2041 is 
capable of delivering a peak power of 180 kw, an average power of 1 1 kw, with a power 
gain of 20 db and an efficiency in excess of 50 per cent at 450 Mc. It is claimed 80 that 
this tube should perform creditably at frequencies up to at least 900 Mc since its 
continuous-power progenitor has been tested at these frequencies. 

The unit-tube principle described above for the beam-power tetrode has been applied 
to other electron-optical geometries such as the tetrode and triode. 80 

Single-ended and Double-ended Configuration. 60 '** A longitudinal cross-sectional 
view of the output circuit of a triode operating in a classical single-ended circuit arrange- 
ment is shown in Fig. 6.26a. The single-ended tube can be considered as a coaxial 
transmission line, consisting of a cylindrical tube with a transition to a short, radial 
cavity external to the vacuum envelope. The maximum voltage exists at the center of 
revolution between the points £and V. The loci of maximum current lie in a horizontal 
plane /. Since the points of maximum voltage and. maximum current are separated by 
a quarter wavelength, the single-ended circuit in a coaxial configuration is a figure of 
revolution whose electrical length is a quarter wave. The RCA 6952 mentioned above 
is an example of a single-ended tube. 

The output circuit of a double-ended tube is shown in Fig. 6.26b. In essence, a 
double-ended tube is two single-ended tubes butted together at their high voltage ends 
EV. The maximum voltage in the double-ended configuration appears in the active 
portion of the tube, whereas it appears outside the active region in the single-ended 
configuration. It is desirable to operate with the maximum voltage in the active 
portion in order to achieve maximum effectiveness. It can be seen that the active 
length of C-D in the double-ended tube can be twice that of the single-ended configura- 
tion ; therefore at least twice the power output can be obtained as compared with the 
single-ended tube. In addition, it is possible to design the double-ended tube with a 
larger diameter before moding problems enter because of the elimination of the so- 
called "deadhead" space which exists in the single-ended tube between the upper 
portion of the active region and the position of the voltage maximum, EV. 

Only the output circuits are shown in Fig. 6.26a and b. Similar arrangements must 
be provided for the grid-cathode input circuit. 




Fig. 6.25. RCA type 6952 tetrode. 



Sec. 6.6] 



Radar Transmitters 



239 




Plate 
cylinder- 



Vacuum envelope 




Plate 
cylinder 



Grid 
cylinder 



Vacuum envelope 



Fig. 6.26. (a) Longitudinal cross-sectional sketch of the output circuit for a triode tube arranged in 
"single-ended" circuitry. Direct-current plate-voltage blocking capacitors and power-output cou- 
pling circuitry not shown, (b) Longitudinal cross-sectional sketch of the output circuit for a triode 
tube arranged in "double-ended" circuitry. (From Hoover* 1 Proc. IEE.) 



Superpower UHF Triode. One of the largest UHF power generators suitable for 
radar application is the RCA developmental type A2346 triode shown in the photograph 
of Fig. 6.27. This double-ended power tube employs 96 unit triodes arranged on a 
6. 6-in. -diameter cylinder and has an active electronic length of 4 in. A cross-sectional 
sketch of the unit triodes employed in this tube is shown in Fig. 6.28. The grid wires 
are wound at a pitch of 72 turns per inch, and the grid wire to filament-strand spacing is 
0.015 in. The grid-plate spacing is about 0.275 in. The electronics of this unit UHF 
triode is similar to that of the original DeForest Audion, yet it is capable of producing 
some of the highest powers obtainable with electronic tubes at UHF frequencies. 

The A2346 is capable of generating 500 kw of CW power at a frequency of 500 Mc 
when operated as a cathode-driven (grounded-grid) amplifier. The power gain is 
about 1 3 to 1 5 db with a conversion efficiency of 50 per cent. In long-pulse operation 
(2.0-msec pulses at a prf of 30 cps), the tube is capable of developing 5 Mw of peak 
power with a 0.06 duty factor at frequencies below 500 Mc. In short-pulse application 
(10 ,usec pulses at a duty factor of 0.01), the A2346 can develop a peak power of 10 Mw. 
Although a 2-msec pulse might be too long for many radar applications, it is well suited 
for radars whose targets are extraterrestrial, as described in Chap. 14. 

Triode vs. Tetrode. M ' 7S > S5 Both the triode and the tetrode have been used as the 
basis for high-power-tube design at UHF. The choice between the two types is a 
difficult one. Both operate by grid control of space current, and many design features 
are common to both. The tetrode has slightly higher gain than the triode, so that less 



240 



Introduction to Radar Systems 



[Sec. 6.6 

driving power is required for a given output. The additional grid of the tetrode gives 
greater isolation between input and output and reduces internal feedback effects. The 
output capacity of the tetrode is lower because of the increased screen-to-plate spacing. 
The bandwidth is also greater because of the greater spacing. On the other hand, the 
additional grid of the tetrode requires a more complex construction than the triode and 




Fig. 6.27. RCA developmental type A2346 superpower UHF triode. 



Liquid cooling 
applied here 



Copper 
plate 




Grid wires 



Wire-support fin 



i Thoriated-tungsten 
filamentary cathode 



Grid liquid cooling 
applied here 



Fig. 6.28. Cross-sectional sketch of unit triodes for UHF power tubes. (From Hoover,"* Proc. IEE.) 

there is some loss of space current to the additional grid. There is also the possibility 
that the tetrode performance will deteriorate because of unforeseen parasitic oscillations 
which might be generated in the cavity between the two grids. Although it may be 
dangerous to generalize, it seems that if a choice must be made between the two, the 
tetrode is the preferable configuration for moderate-to-large powers while the triode is 
to be preferred at the highest power levels. 



Sec. 6.6] Radar Transmitters 241 

The Resnatron. The resnatron is a particular form of tetrode characterized by ( 1 ) the 
RF circuitry located completely within the vacuum envelope, (2) the control grid and 
the screen grid operated at RF ground (grounded-grid tetrode), and (3) the screen grid 
operated at the same d-c potential as the anode. The resnatron was the first high-power 
tube capable of delivering tens of kilowatts of average power at UHF. Although it has 
seen but limited application in the past, it is of interest not only for historical reasons, 
but also because it is a potentially useful device for obtaining high power. 

By placing the resonant circuits, the bypass capacitors, and the RF isolation chokes 
all within the vacuum system of the tube, the d-c voltage-supply leads do not become a 
part of the resonant circuits. Therefore the inductance of the supply leads has a 
negligible effect on the operation of the tube. The RF and the d-c portions of the 
circuit are separated from one another just as they are in the magnetron, klystron, or 
traveling- wave tube. Another benefit of placing the RF circuitry within the vacuum is 
that dielectrics such as glass or ceramics are external to the fields which could cause 
dielectric heating losses. These characteristics make the generation of high power at 
high frequencies easier than with the conventional grid-controlled structure. 

The resnatron has been operated in the past as a grounded-grid (cathode-driven) 
amplifier, although a grounded-cathode (grid-driven) tube is capable of higher gain. 
However, the grounded-cathode amplifier requires that the screen grid be bypassed to 
the cathode by some means, and in the high-power resnatron this presents tedious 
design problems. 

Operating the resnatron with the screen grid and plate at the same d-c potential 
eliminates the need for a d-c blocking capacitor between the screen grid and plate, as 
required in the classical operation of tetrodes. A further advantage of operating the 
screen grid at high d-c potential is that the effects of electron transit time are reduced. 

The resnatron was originated about 1938 by Sloan and Marshall 86 at the University 
of California. Their original objective was to develop a high-power oscillator in which 
the phase delay caused by the transit time was compensated by introducing the proper 
phase shift in the feedback circuit. They achieved an average power of 8 kw at a 
frequency of 860 Mc. During World War II, Salisbury and associates at the Harvard 
Radio Research Laboratory developed a high-power CW resnatron for jamming 
application. 81 ' 87 ' 88 The resnatron was operated as a self-excited oscillator. It was 
used operationally by troops in the field as a jammer with a noise-modulated bandwidth 
of 4 Mc. In the laboratory it was also operated as a power amplifier, particularly of 
the class C type. When used as an amplifier instead of an oscillator, it is not necessary, 
nor is it desirable, for the transit time to play the same role that it played in the Sloan and 
Marshall oscillator. 

The input cavity of the Harvard tube was placed between the control grid and the 
filament structure, while the output cavity was between the screen grid and the anode. 
The tube delivered more than 50 kw of output power with a 60 to 70 per cent plate 
efficiency and could be tuned over a frequency range of 350 to 650 Mc. As an amplifier 
the power gain was 10 db. The amplifier efficiency was the same as the self-excited 
oscillator. Plate voltages of the order of 15 kv were employed for maximum power 
output. In its day, this tube represented a considerable increase in power capability 
over any other tube which operated at frequencies as high as UHF. Even by present 
standards the 50 kw delivered by this resnatron is quite a lot of power. 

The resnatron tubes were operated "on the pumps"; that is, they were continuously 
evacuated in order to maintain the vacuum. The tubes could not be sealed off since 
they were too big to be made to hold a vacuum with the techniques available at that time. 
There is no reason to believe that sealed-off resnatron tubes could not be built if suffi- 
cient development effort were applied. Even with continuous pumping the vacuum 
inside the tube was relatively poor, limiting the life of the pure tungsten cathodes. The 



242 Introduction to Radar Systems [Sec. 6.6 

tubes were designed to be readily taken apart for replacing the cathodes. In spite of 
the fact that these tubes were not small, that they had to be continuously pumped, and 
that they had to be periodically dismantled to have their cathodes replaced, they were 
operated successfully in truck-borne units during wartime conditions by army troops 
with no special educational background. 

The Harvard RRL resnatron' described above was designed with a radial electron 
flow; that is, the electron beam was perpendicular to the axis of symmetry of the 
cylindrical tube structure. Tubes operating with axial flow in which the electron 
stream is directed parallel to the axis of symmetry have also been built. 89-91 The tube 
described by Sheppard et al. 90 used a reflex principle of operation in combination with 
the axial geometry of the electron flow. The reflex resnatron is similar to the con- 
ventional resnatron except that the anode is replaced by an electrode of sufficiently 
negative potential which repels the electrons and bends them back toward the screen, 
where they are collected. The advantage claimed for the reflex resnatron is that 
wideband modulation may be obtained with low modulation power by swinging the 
repeller voltage. Being negative, the repeller collects little or no current. Hence the 
modulation power may be small. In one experimental device a power output of 2.6 kw 
was obtained at a frequency of 560 Mc, with a power gain of 5, an efficiency of 38 per 
cent and a bandwidth of 8 Mc. 

The performance obtained with the axial-flow resnatron described by McCreary et 
al. 89 was similar to the performance achieved with the World War II radial-flow 
resnatron of Salisbury. A CW power output of 29 kw was obtained at a frequency 
of 420 Mc with power gains in excess of 10 db and an estimated bandwidth of 4 Mc. 
The plate efficiency varied from 45 to 75 per cent, depending upon the operating point 
of the tube. The advantage claimed for the axial-flow resnatron is its simpler con- 
struction as compared with that of a radial-flow tube. 

An interesting application of the resnatron and one analogous to the type of operation 
which might be encountered in radar is its use as a high-power pulse amplifier for the 
University of Minnesota linear proton accelerator. 92 These tubes operate at a fre- 
quency of 202 Mc and deliver a peak power of 3.5 Mw and an average power of 63 kw. 
The pulse width is 300 /^sec at a prf of 60 cps (duty cycle of 0.018). A power gain of 
10 db was achieved with an efficiency of 62 per cent. The plate voltage required for 
this power output was 70 kv, and plate current was 8 1 amp. This particular resnatron 
utilized a radial-flow geometry. The cathode consisted of 36 strands of pure tungsten 
with approximately 5 in. of emitting length per strand. Thus the tube actually con- 
sisted of 36 unit tetrodes operating in parallel. All RF cavities, tuners, water-cooling 
coils, and a 100-kv isolating choke were located within the vacuum enclosure. As with 
other high-power resnatrons, the tube construction precluded any real bake-out and 
outgassing, and the tubes had to operate "on the pumps." Exclusive of the 1,400-cfm 
oil-diffusion vacuum pump, the tube weighed 2.5 tons and stood 15 ft. The tubes 
could be readily dismantled for filament replacement or other repairs. The tungsten 
filaments in the tube had to be replaced on the average of every 900 hr. Four such 
resnatrons were used in the linear proton accelerator. Three were power amplifiers, 
each operating into high-g accelerator tank circuits, while the fourth acted as a driver 
for the other three. 

The resnatrons which have been described all operated in the UHF portions of the 
frequency band. A number of experimental microwave resnatrons have been built at 
a frequency of 3,000 Mc. These are mentioned by Hoover, 80 who quotes a personal 
communication from Dr. D. H. Sloan of the University of California. Sloan and his 
associates were able to achieve a peak power of I Mw at S band with a 100-^sec pulse 
width. The efficiency was better than 50 per cent. Sloan claimed that the basic 
structure could, with minor modifications, be made to deliver 1 Mw of power. In 



Sec. 6.6] 



Radar Transmitters 



243 



another design, a peak power of 1.5 Mw was obtained with a 2-fj.sec pulse width. It 
was thought that this tube should have delivered 5 Mw, except that the particular 
cathode used in this tube warped. It was claimed that power gains of 10 to 30 db are 
obtainable and that the average pulse or the maximum C W power can reach hundreds of 
kilowatts. 80 - 93 

Tube Protection. 9 * It is possible for power tubes to develop internal flash arcs with 
little warning even though they are apparently of good design and operated in a con- 
servative manner. This type of unexpected arc discharge is known as the Rocky Point 
effect. Its name is derived from experiences with power tubes for communications 
transmitters at Rocky Point, Long Island, New York. When a flash arc occurs in an 
unprotected tube, the rectifier and filter-capacitor bank discharge large currents through 
the arc and the tube can be easily damaged. The mechanism of the Rocky Point effect 



AC 



Circuit 
breaker 



-^-nm^ 



Rectifier 



Electronic 
crowbar 
gas tube- 




Overlood-^ML^ 
relay _J_ 



Fig. 6.29. Simplified diagram of electronic-crowbar fault-protection circuit. (Reprinted, by permis- 
sion, from the January, 1956, issue of Electronics, a McGraw-Hill publication, copyright, 1956.) 



does not seem to be well understood, but it is believed that it can be triggered by sources 
ranging from cosmic rays to line-voltage transients, parasitic oscillations, spurious 
renegade primary and secondary electrons, material whiskers, and photoelectrons. 

Tubes may be protected from the damaging effects of arc-discharge currents by 
diverting the damaging current from the tube. One such protection device is called an 
electronic crowbar. It places a virtual short circuit across the rectifier output similar to 
that placed on the rectifier by the flash arc. The short-circuit current is transferred to a 
gas-discharge tube such as a hydrogen thyratron or an ignitron which is not damaged 
by the momentary short-circuit conditions. 

The principle of operation of the electronic crowbar is illustrated by the diagram 
of Fig. 6.29. When a fault occurs in the protected power tube, the sudden increase in 
current through the cathode resistor R k produces a positive voltage pulse which is 
coupled by C e to the grid of the electronic-crowbar gas tube, here shown as a thyratron. 
This impulse causes the thyratron to conduct. The low impedance of the thyratron 
when conducting results in the damaging current being shunted away from the power 
tube and through the thyratron crowbar tube. The surge of current through the crow- 
bar tube actuates the overload relay, which in turn opens the circuit breaker and 
deenergizes the primary source of power. A small series resistor R provides adequate 
voltage across the crowbar tube to ensure its conduction despite severe low-impedance 
flash arcs in the protected tube. In a typical large power-tube installation the value of 
the series dropping resistor is only about 5 ohms. 

The electronic crowbar is capable of providing fault protection within 1 to 5 ,asec 
after the detection of the fault. The high-speed protection of this device permits safe, 
full-power operation of the power tube almost immediately after the arc is quenched. 



244 Introduction to Radar Systems [Sec. 6.7 

6.7. Comparison of Tubes 

No one single tube is best suited for all radar applications. In this section the 
characteristics of the various radar power tubes will be compared and those factors 
which influence the selection of one tube instead of another will be discussed. 

Before proceeding it might be worthwhile to inject a word of caution concerning the 
type of comparison presented here. It is not meant to convey the impression that some 
tubes should always be used in radar to the exclusion of others. The characteristics of 
each tube are sufficiently different so that each has its own area of application for which 
it is preferred. Tubes for radar transmitters are continually being improved, and new 
principles of RF power generation will no doubt be discovered in the future. The 
discussion of tube technology presented here, as with any component technology which 
is continuing to expand and grow, is only valid as of the time of writing. The con- 
clusions presented should therefore be considered as subject to revision as new develop- 
ments are reported. 

Oscillators vs. Amplifiers. The various tubes considered for RF power generation 
may be classified as either self-excited power oscillators or as power amplifiers driven 
by stable low-power oscillators. The magnetron and the Stabilitron are self-excited 
power oscillators, while the klystron, traveling-wave tube, Amplitron, and grid- 
controlled tubes are examples of power amplifiers. The physical size of a transmitter 
using a power oscillator is usually smaller than that of a power amplifier. This is of 
advantage for radar applications in which mobility is required, but in general, it also 
means that the maximum power output available from a small-size tube is less than 
from one of larger size. 

The frequency stability of a high-power self-excited oscillator is not as good as that 
of an amplifier driven by a stable, crystal-controlled low-power oscillator. A high-g 
cavity can be used to improve the self-excited oscillator frequency stability, but the 
stability is usually less than that obtained with the master-oscillator power amplifier. 
In the Stabilitron the stabilizing cavity is placed at the input and permits more efficient 
operation than if it were in the output. The magnetron oscillator frequency can also 
be stabilized with an external cavity, but it would have to be placed at the output with a 
corresponding reduction in over-all efficiency. 

Good frequency stability is of importance for MTI radar. If the frequency of 
oscillation wanders excessively during the interpulse period, poor subclutter visibility 
results. The good stability of the amplifier plus the fact that the transmitted waveform 
is generated at low power level means that it is easier to achieve the sophisticated 
modulations required for pulse compression with amplifiers than with oscillators. 
Since amplifier MTI radars are coherent from pulse to pulse, wth-time-around echoes 
from fixed targets are eliminated. This is not true with oscillator MTI radars since 
they are coherent only over the duration of one pulse-repetition period. 

The superior frequency stability and higher power output of the power amplifier are 
accompanied by a larger and heavier transmitter. In addition to the power tube 
itself, a stable, crystal-controlled oscillator, a frequency multiplier chain, and driver 
amplifier stages are needed to amplify the power to the level necessary to drive the final 
tube. The driver stages of the high-gain klystron or traveling-wave tube may be 
relatively modest, especially in those tubes with gains of the order of 50 to 60 db. The 
Amplitron, on the other hand, is a relatively low gain tube, values of 8 to 10 db being 
typical. The low gain means that two or three high-power Amplitrons might have to 
be operated in cascade to achieve a reasonable over-all gain. As mentioned previously, 
one of the applications of a low-gain, high-power, high-efficiency tube like the Amplitron 
is as a booster to increase the range of lower-power radar sets. 

Other advantages of the amplifier over the oscillator are that the amplifier is less 



Sec. 6.7] Radar Transmitters 245 

affected by imperfections in the modulator and it is not subject to long-line effect. 
Power amplifiers may also be combined to deliver more power than is possible with a 
single "bottle." 95-97 The hybrid junction can be used to combine tubes in pairs; that 
is, the number of tubes combined is given by 2" (or 2, 4, 8, 16, etc). 

In general, the power amplifier is probably to be preferred over the power oscillator 
for most radar applications in which high power and/or good MTI performance is 
desired. On the other hand, if size, weight, and complexity are important considera- 
tions, as they are in many applications, a magnetron oscillator would be preferred even 
at the sacrifice of radar performance. 

Comparison of Power Amplifiers. A comparison of power oscillators will not be 
given here since the two oscillators most suited for radar application, the magnetron 
and the Stabilitron, were compared in the previous section. In the remainder of this 
section, the characteristics of various power amplifiers will be compared. The tubes 
which will be considered include the grid-controlled amplifier, the klystron, the traveling- 
wave tube, and the Amplitron. 

1 . frequency range. With the exception of the grid-controlled tube, there seems 
to be no reason why the amplifier tubes discussed in this chapter could not be designed 
to operate anywhere within the normal radar frequency range from UHF to K band. 
The grid-controlled tube is capable of exceptionally high power output at UHF or lower. 
They are not often used above L band, although resnatrons have been operated experi- 
mentally at Sband with respectable power output. The power output of any particular 
tube type^vvill be less at the higher frequencies than at the lower frequencies. The 
power variation with frequency is not always a simple one, but in general, it seems to 
vary inversely as the square of the frequency. 

2. power. In principle, all the amplifier tubes which were considered are capable 
of generating relatively large average power. However, the traveling-wave tube does 
not seem to be able to achieve as large a power output in practice as some of the other 
more narrowband tubes, without a corresponding sacrifice in the bandwidth. This 
conclusion could very well be changed in the future since there is no fundamental 
reason why the power output of a traveling- wave tube should be significantly less than 
that of a klystron. The grid-controlled tube, the klystron, and the Amplitron are all 
capable of generating tens or even hundreds of kilowatts of average power. For 
comparison, a good average power for a magnetron oscillator is a few kilowatts. The 
high efficiency of the Amplitron is one reason why it is capable of much larger power 
than, for example, the relatively low efficiency traveling-wave tube. 

All tubes seem to suffer the same peak-power limitations imposed by voltage break- 
down in waveguides or cavities. The peak-power limitation due to voltage breakdown 
also varies inversely with the square of the frequency. 

3. efficiency. A high efficiency is one of the important attributes of a good power 
tube. The greater the efficiency, the greater the power output for a structure of a given 
size and the easier it will be to dissipate the heat generated by the losses. The more 
efficient tube requires less prime power for a specified power output, and the operating 
costs are less. The efficiency usually quoted in this chapter is the RF conversion 
efficiency, defined as the ratio of the RF power output available from the tube to the d-c 
power input of the electron stream. The conversion efficiency is the product of the 
electronic efficiency times the circuit efficiency. The electronic efficiency is equal to the 
RF power delivered by the electron beam to the circuit, divided by the average power 
supplied to the electron beam. The circuit efficiency is the fraction of RF power 
going into the resonant system which appears as output power; the remainder is wasted 
as heat because of copper losses. A more complete measure of transmitter efficiency 
from the operational point of view would be the ratio of the RF power output to the 
total power input. This is over-all efficiency. The power input would include all 



246 Introduction to Radar Systems [Sec. 6.7 

power needed for the operation of the tube such as heater power, power for cooling 
devices, and the power required for electromagnets if used. The RF conversion 
efficiency for a typical high-power klystron might be 35 to 45 per cent, but the over-all 
efficiency might be 25 per cent. 

The Amplitron seems to be capable of higher efficiencies (70 to 90 per cent) than any 
of the other amplifiers discussed. The efficiency of the grid-controlled tube is slightly 
less. The klystron has a lower efficiency, but the traveling-wave tube has the lowest of 
all. Typical magnetron oscillator efficiencies vary from 35 to 60 per cent, which is in 
between the efficiencies of klystrons and grid-controlled tubes. 

In general, crossed-field devices such as the magnetron or the Amplitron have higher 
efficiencies than collinear beam devices such as the klystron or the traveling-wave tube. 
In the collinear beam device no additional kinetic energy is supplied to the beam after it 
enters the interaction space. The d-c energy from the power supply must all be 
converted into kinetic energy of motion before conversion to RF energy can occur. 
On the other hand, there is direct conversion of potential energy to RF energy in the 
crossed-field device. The electrons perform work on the RF field as they sacrifice their 
energy of position and drift to the collecting electrode (anode). 

4. gain. The tube with the highest gain is the klystron. Gains of the order of 60 db 
or more are not uncommon with four-cavity, synchronously tuned klystrons. The 
Amplitron has the lowest gain of the amplifier tubes discussed here, with typical values 
of from 8 to 10 db at high power levels. The grid-controlled tube with values from 10 
to 25 db is slightly better than that of the Amplitron. The gain of the traveling-wave 
tube is better than that of the grid-controlled tube, but less than that of the multicavity 
synchronously tuned klystron. 

The higher the gain of the power tube, the smaller the power required of the source 
which drives the amplifier. Only a modest driver is required for the klystron, but the 
driver of the Amplitron, for example, might represent a substantial fraction of the total 
transmitter. The driver of low-gain tubes often has to be another power tube of the 
same capabilities as the output power tube. 

5. bandwidth. The traveling-wave amplifier is theoretically capable of large 
bandwidth. The bandwidth of practical traveling- wave tubes is of the order of 10 per 
cent or more at high power levels. This is followed closely by the Amplitron, with 
bandwidths of about 7 to 10 per cent. The multicavity klystron can also be made to 
have a respectable bandwidth by stagger tuning the various cavities and trading gain for 
bandwidth. Bandwidths from 3 to 5 per cent are possible with the klystron and might 
be as high as 12 per cent or more. The bandwidth of the grid-controlled tube is the 
smallest of all. It is determined by the loaded Q of the output cavity. Although 
bandwidths of the order of 1 to 2 per cent are common, large bandwidths may be possible 
with broadband cavities within the vacuum envelope. 

A broad-bandwidth transmitter is important in radar applications in which accurate 
range measurement or good range resolution is necessary or where it is required to 
change frequency rapidly over a wide frequency band. 

6. size and weight. The klystron and the traveling-wave tube are the heaviest and 
the biggest of present radar power tubes. The need for an electromagnet and lead 
shielding greatly adds to the weight. The Amplitron with permanent magnet is lighter 
than the klystron or the traveling-wave tube, but is heavier than the grid-controlled tube, 
which is the lightest of all. 

The size and weight of a particular tube are probably not as important to the radar 
engineer as is the total weight of the transmitter. The total weight depends on the gain 
and efficiency of the tube, the type of modulator, the cooling requirements, and the 
particular operating voltages and currents. Extremely high anode voltages as in the 
klystron and traveling-wave tube require lead shielding to attenuate harmful X-ray 



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248 Introduction to Radar Systems [Sec. 6.8 

radiation generated by the tubes. High voltages also require good insulation of the 
equipment and cables. If, as in grid-controlled tubes, large heater currents are 
necessary, large low-loss conductors or cable must be used for transmitting these high 
currents. 

No general statement can be made regarding the over-all size and complexity of radar 
transmitters employing power 'amplifiers because of the many factors involved. 

7. life. The life of the klystron and the traveling-wave tube can be relatively high 
when compared with other high-power tubes. A life of 5,000 to 10,000 hr seems to be 
typical. (There are 8,760 hr in a year.) The life of a grid-controlled tube is equally 
good. The Amplitron life is claimed to be greater than 1,000 hr, while the life of 
high-power magnetron oscillators is of the order of 1,000 hr, or perhaps less, especially 
at the higher frequencies. Magnetrons such as the E.E.V. (English Electric Valve 
Company) type 7182, however, have lives of the order of 10,000 hr. The life of any 
particular tube will also depend upon how close to rated maximum power output it is 
operated. 

Long life is desirable in order to minimize equipment downtime for repair. In 
addition, the excessive replacement of tubes adds to the operating cost. 

8. table of comparison. In Table 6.4 are listed typical operating characteristics of 
representative power-amplifier tubes. With the exception of the grid-controlled 
tetrode, all operate at S band. The power output of these amplifiers is roughly com- 
parable except for the SAS-61. This is a medium-power tube, which may be used for 
medium-power radar applications or as a driver tube for higher-power amplifiers. It 
is included in this table since it is an example of a space-charge-focused klystron, 
whereas the other klystron entry, the VA-820, is focused with an external electro- 
magnetic focusing coil. 

6.8. Modulators 98 " 101 

The modulator is the device which turns the transmitting tube on and off in such a 
manner as to generate the desired waveform. When the transmitted waveform is a 
pulse, the modulator is sometimes called apulser. Each RF power tube has its own 
particular characteristics which determine the type of modulator. The magnetron 
oscillator, for instance, is plate-modulated, so that the modulator must be designed to 
handle the full pulse power. On the other hand, full beam power of the klystron and 
the traveling- wave tube can be switched by a modulator handling a small fraction of the 
total beam power, if the tubes are designed with modulating anodes and provided the 
interpulse noise due to electrons leaking through the modulating anode is small com- 
pared with receiver noise. Otherwise plate modulation is necessary. 

Low-power grid modulators can be used with grid-controlled tubes such as the triode 
and the tetrode. Screen-grid pulsing may also be employed in a tetrode. In those 
applications where the number of electrons which escape the cutoff action of the grid 
are large enough to induce a significant shot noise in the plate circuit, plate modulation 
must be employed to ensure that interpulse noise does not degrade the sensitivity of the 
receiver. For this reason grid-controlled tubes are sometimes plate-modulated. 
Although plate modulation requires considerably higher modulation power than grid 
modulation, it completely eliminates interpulse noise and improves the operational 
stability as regards missing pulses. 

The number of electrons which manage to leak through the modulating anode of 
klystron amplifiers when it is cut off is claimed to be negligible for most radar applica- 
tions. 102 In one type of klystron amplifier the interpulse noise due to electrons leaking 
past the modulating anode is stated to be at least 170 db below the pulse power level as 
measured over a 25-kc bandwidth. 

The Amplitron and the Stabilitron are plate-modulated similar to the magnetron. 



Sec. 6.8] 



Radar Transmitters 249 



The basic elements of one type of radar modulator are shown in Fig. 6.30. The 
modulator consists of a charging impedance, an energy-storage element, and a switch. 
The energy for the pulse is supplied from an external source. It is accumulated in the 
energy-storage element at a slow rate during the interpulse period. The charging 
impedance limits the rate at which energy can be delivered to the storage element. At 
the proper time, the switch is closed and the stored energy is quickly discharged through 
the load, which might be a magnetron, in a relatively short time to form the pulse. 
During the discharge cycle, the charging impedance prevents energy from the storage 
device from being dissipated in the source. 

The energy-storage element might be either electrostatic (basically a capacitance) or 
electromagnetic (inductance). The former is more often used in practice since it is 
easier to implement. 98 The configuration of Fig. 6.30 is that of a voltage-fed modulator 
using an electrostatic storage element. 



Energy 
source 



Charging 
impedance 



I 



^. 



Switch\ I 



zT 



Energy 
storage 
element 



i I 



! I 



Load 



Charging path x ^-Discharge path 

Fig. 6.30. Basic elements of one type of radar pulse modulator. 



The simplest electrostatic storage element is a capacitor. A simple capacitor has the 
disadvantage, however, that the energy discharges exponentially with time and 
produces a poor pulse shape. To obtain a relatively flat pulse from the discharge of a 
capacitor, the time constant of the discharge circuit must be large compared with the 
desired pulse duration and the switch must be capable of interrupting the discharge as 
well as initiating it. A vacuum tube can be used for this purpose. Only a small 
portion of the stored energy in the capacitor is expended during the switching. 

A gas tube such as the thyratron or the ignitron is capable of handling highpowerand 
presents a low impedance when conducting. However, a gas tube cannot be turned 
off once it has been turned on unless the plate current is reduced to a small value. This 
is unlike the operation of the vacuum tube, which can be turned off or on with essentially 
equal facility. Once the thyratron is triggered by its grid, it cannot be shut off until the 
storage element completely discharges itself. For this reason a capacitor is not a 
satisfactory storage element to use with a gas-tube switch since the discharge pulse 
cannot be made rectangular. However, a delay-line storage element can produce a 
rectangular pulse and is satisfactory for use with a gas-tube switch. An open-circuited 
delay line of length t/2 will, upon discharge, generate a pulse of width t. The modulator 
containing a gas-tube switch and a delay line as the energy-storage element is called a 
line-type modulator. It is commonly employed with high-power magnetrons. The 
delay line of the line-type modulator is called the pulse-forming network and is abbrevi- 
ated PFN. 98 - 103 

In the remainder of this section the three basic types of radar modulators which may 
be used to pulse the magnetron oscillator will be discussed. These are ( I ) the line-type 
modulator with a gas-tube switch and a delay-line storage element, (2) the pulsactor, 
which uses saturable reactances for both switching and storage purposes, and (3) the 
hard-tube modulator incorporating a vacuum-tube switch and capacitor storage 



250 Introduction to Radar Systems 



[Sec. 6.8 



element. The effect of modulator pulse shape on the magnetron R.F pulse will also be 
discussed. 

Line-type Modulator. A diagram of a line-type pulse modulator is shown in Fig. 
6.31. 104 The charging impedance, shown as an inductance, limits the rate at which 
current is drawn from the energy source during the charging cycle. It also acts as an 
isolation element during the discharge cycle and prevents the pulse-forming network 
from discharging into the energy source instead of into the useful load. These functions 
of the charging impedance could just as well have been obtained with a resistance, 
except that the maximum efficiency would then be 50 per cent, since half the charging 
energy would be dissipated in the resistance. A pure inductance absorbs no energy and 
is preferred in high-power applications. 



?,ȣ. Ch-tfn, 



i — nftowip- 



Energy 
source „ 



diode 
-M- 



Trigqer_^_ 



Hydrogen 
thyratron 



. Bypass 
■ diode 



Pulse-forming network 

c TTTT T 




Magnetron 



Damping 
network 



Fig. 6.31. Diagram of a line-type pulse modulator. 



I. 



■^WiTOWJo^ *\- 



The energy-storage element, or pulse-forming network, is usually a lumped-constant 
delay line. It consists of an air-core inductance with taps along its length to which are 
attached capacitance to ground. The number of taps depends upon the pulse width 
and the fidelity required. The impedance level of the line is chosen to fit the charac- 
teristics of the load, the switching tube, and the power supply. Some degree of 
flexibility is permissible in the selection of the delay-line impedance since a transformer 
may be used to match the delay line to that of the load. It is sometimes convenient to 

design the delay line for an impedance of 50 ohms so 
as to make it unnecessary to match the delay line to 
the transmission cable, which is usually 50 ohms 
impedance. The transformer would then be used 
to match the cable impedance to the impedance of 
the magnetron, which might be of the order of 500 
to 1,000 ohms. A perfect match is not possible in 
all cases since the magnetron impedance is non- 
linear. 

The equivalent modulator circuit during the charging cycle is shown in Fig. 6.32. 
The delay line is represented by its capacitance only, since the inductance of the line is 
negligible compared with the charging inductance. The load is represented by a 
resistance R. The effect of the charging diode may be ignored for the moment. The 
charging inductance L C h and the delay-line capacitance C form a resonant circuit. If a 
d-c voltage is suddenly applied to the input, oscillations will occur provided 
(Leh/C)- > R/2. For small values of R, the frequency of oscillation will approach the 
value / = {2ir)~ 1 (L C hC)~ i . The peak voltage across the delay-line capacitance C 
will be twice the supply voltage after the first half cycle of oscillation. Thus the pulse 
repetition frequency/,, will be twice the resonant frequency/ , or l// r = T B = 77(L C hC) i , 
where T v is the pulse-repetition period. This method of operation, ignoring the effect 
of the charging diode, is called d-c resonant charging. 



Fig. 6.32. Equivalent circuit of the 
modulator of Fig. 6.31 during the 
charging cycle. 



Sec. 6.8] Radar Transmitters 251 

A disadvantage of d-c resonant charging is that the pulse repetition frequency is fixed 
once the values of the charging inductance and the delay-line capacitance are fixed. 
The charging, or hold-off, diode inserted in series with the charging inductance (Fig. 
6.31) permits the modulator to be readily operated at any pulse repetition frequency, 
which is less than the prf as determined by the resonant frequency f . The function of 
the diode is to keep the delay line from discharging until the thyratron fires. 99 ' 105 

If a mismatch occurs during the discharge cycle, a charge might be placed on the 
delay-line capacitance with polarity opposite to that normally placed on the capacitance 
during the charge cycle. This charge cannot be dissipated by the thyratron since its 
polarity is opposite to that needed to cause conduction. A small reversed voltage 
remains on the delay line. This voltage is in series with the d-c voltage of the power 
supply at the start of the next charging period. If the charge were allowed to remain, 
the peak voltage on the network would increase with each cycle and build up to an 
abnormally high value, with the possibility of damaging the thyratron by exceeding its 
permissible operating voltage. The inverse charge may be dissipated by connecting a 
bypass diode and a series inductance L B in parallel with the thyratron as was shown in 
Fig. 6.31. The diode conducts whenever an inverse voltage appears on the capacitance. 
The series inductance L B , the inductance of the transformer primary, and the capacitance 
C form a resonant circuit that gives rise to an oscillation that reverses the voltage on the 
capacitance. The polarity of the voltage reverts to the normal direction, and excessive 
build-up is prevented. 106 

The magnetron is a nonlinear impedance and will not be matched to the line under 
all conditions. The mismatch can cause a spike to appear at the leading edge of the 
pulse. The spike can be minimized by introducing an RC circuit in parallel with the 
primary as shown in Fig. 6.31. This is called the despiking circuit. The resistance is 
chosen equal to the impedance of the pulse-forming network, and the capacitance is 
chosen small enough so as to be almost completely charged after the oscillator draws 
full-load current. 99 

The function of the damping network is to help reduce the trailing edge of the voltage 
pulse and prevent postpulse oscillations which could introduce noise or false targets. 

The pulse modulator described above was assumed to operate from a d-c power 
supply. Alternating current could also be used. 99 

Switching Devices for Line-type Modulators. Most of the switching devices for 
line-type modulators are based on gas-discharge phenomena. Gas-discharge devices 
have the advantage of relatively low impedance during the conduction state and can 
handle considerable power. Two gas-discharge switches used in early radar modu- 
lators were the rotary spark gap and the enclosed, fixed spark gap. These two devices 
do not seem to be used as frequently in modern radar as the hydrogen thyratron or the 
ignitron. The saturable reactor also may be used as a switch. Each of these has 
different characteristics as concerns life, precision of firing, maximum pulse repetition 
frequency, range of operating frequency, and impedance in the closed position. There 
is no one switching device which is always better than the others. 

The hydrogen thyratron has been widely employed as the switch in magnetron radar 
modulators, although other gas fillings are sometimes used. 107 The advantage of a 
hydrogen-filled thyratron over an inert-gas- or mercury-filled thyratron is the rapid 
ionization and deionization time of hydrogen gas. The hydrogen thyratron also has 
better capacity for high-peak currents and can be designed to be relatively insensitive to 
temperature. 

A semiempirical, semitheoretical parameter which has been used to evaluate the 
capability of thyratrons is the P b factor. 101 It is defined as twice the product of the peak 
output power times the pulse repetition rate in a typical line-type modulator. The load 
impedance is assumed to be equal to the impedance of the line. The /^-factor describes 



252 



Introduction to Radar Systems 



[Sec. 6.8 



the trade-offs which can be made between the peak voltage, peak current, and the pulse 
repetition frequency for a particular thyratron. These three parameters may be 
juggled so long as the P„ factor of the tube is not exceeded. 

Saturable-reactor Modulator. 10S ~ 112 The saturable reactor is an iron-core inductance 
so designed that its magnetic core is driven into saturation for normal values of coil 
current. The incremental inductance is high when the current through the coil is small 
and the core unsaturated, but the inductance is low for large currents when the core is 
saturated. The ratio of inductance in the unsaturated condition to the inductance in 
the saturated condition can be as great as 2,000 or higher when using high-permeability 
nickel-iron alloys. This change in inductance (impedance) may be used as the basis for 
switching action. The advantage of the saturable reactor in radar modulator applica- 
tion is its relatively long life. It is a passive device and uses neither electronic tubes nor 



/ 


Pola 
/wine 


rizing 
inas \ 

JLZ2Z L Z 


Output 










^ 


transformer 


Energy 
source 


_J 


^r J 


| To load 

° 









Fig. 6.33. Two-stage saturable-reactor modulator, or pulsactor. 



mechanical moving parts. Also, the pulse-to-pulse jitter is less than with the thyratron. 
The chief disadvantage of the saturable reactor modulator is its poor and uncontrolled 
pulse shape. 

During the formation of the pulse the reactor becomes saturated and the pulse- 
forming network must discharge through the saturated reactance of the inductor. 
Since the reactance becomes a part of the discharge circuit, it limits the minimum width 
of the pulse. The reactance cannot be made arbitrarily small without permanently 
saturating the core. 110 This limitation may be avoided by operating as indicated in 
Fig. 6.33. The circuit may be considered as a series of saturable reactors arranged in 
resonant circuits in which the networks are charged stage by stage. Two stages are 
illustrated. The optimum number of stages will depend upon the desired width of the 
output pulse. The inductance of each succeeding stage is made lower than that of the 
preceding stage, so that the resonant frequency of succeeding stages is higher. 

Assume that the energy source feeding the modulator is a sine wave whose frequency 
is the same as the desired pulse repetition frequency. The charging inductance Z. C h 
and the capacitance C l form a resonant circuit. Initially, the two inductances other 
than the charging inductance are biased to operate in the unsaturated condition and 
have high reactance. For this reason they have no effect on the initial charging action. 
Since the resonant circuit consisting of L C h and C\ is excited at its resonant frequency, 
the voltage at B, in Fig. 6.33, across the capacitor C x builds up to a maximum equal to 
■n times the input voltage at A. 

When the voltage across the capacitor Q reaches a maximum, the inductance L x 
saturates and its reactance is lowered to a considerably smaller value L ls . The switching 
action of L x allows the charge on C 1 to transfer to C 2 . This is indicated by the current 
i C2 in Fig. 6.34. The combination of L ls , C 1; and C 2 forms a resonant circuit with a 
higher resonant frequency than that of Z, C h and Q, since Q and C 2 are in a series and 
L ls < L C h- The current i C2 rises rapidly. As the current builds up in the resonant 
circuit, the voltage across the capacitor, being 90° out of phase with the current, decreases 
and the inductance Lj returns to its unsaturated state. The voltage across C 2 reaches a 



Sec. 6.8] 



Radar Transmitters 



253 



maximum at the same time that L 2 saturates. The energy stored in C 2 is then trans- 
ferred to the load via the current i C3 , which is the output pulse waveform. In essence, 
the chain of saturable reactors acts to compress the energy-transfer interval, increasing 
the peak power and decreasing the pulse duration from stage to stage. 

The output waveform is more like that of a resonant sine wave than a rectangular 
pulse. This shape is not always well suited to radar application and is one of the 
limitations of this modulator. A more rectangular pulse may be had by tapping 
the last-stage, saturable-reactor winding and adding capacitance to ground so as to 
simulate a lumped-constant delay line. 111 The capacitors from the taps to ground 




Time ■ 



Fig. 6.34. Build-up of the pulse in the two-stage saturable-reactor modulator of Fig. 6.33. 

have negligible effect on the unsaturated operation, but at and during the switching 
operation, they produce an improved output pulse waveform. The output pulse 
width may be changed to some extent by adjusting the polarizing current. 

The nonrectangular pulse shape is not a disadvantage in all cases. A rectangular 
pulse produces a wide spectrum which might cause interference with adjacent frequency 
bands. The frequency spectrum of a rounded pulse will fall off more rapidly on either 
side of the carrier frequency and tends to cause less interference. 

When operating in the manner described above, the saturable reactor performs the 
functions of an inductive component, a switch, and a part of a resonant circuit. When 
used in this trimode capacity it is sometimes called apulsactor. 



Trigger 
from prf - 
generator 



Driver 
(pulse shaping) 



(Video) 
power amplifier 



_To 
"transmitter 



Fig. 6.35. Block diagram of one type of hard-tube modulator. 

Hard-tube Modulator.^ 98 ' 100 ' 113 The hard-tube modulator is essentially a high- 
power video pulse generator. It derives its name from the fact that the switching is 
accomplished with "hard" vacuum tubes as opposed to "soft" gas tubes. A block 
diagram of a particular hard-tube modulator is shown in Fig. 6.35. The trigger pulses 
from the pulse-repetition-frequency generator initiate the driver at the proper instants 
of time. The driver generates the desired pulse waveshape. The waveform generated 
by the driver is amplified by the power amplifier to the level required to pulse the trans- 
mitter. There are any number of pulse-forming circuits which could be used for the 
driver." The design of the power amplifier is similar to the design of conventional 
video amplifiers except that high-power tubes must be used. 

A single high-power tube operating as a blocking oscillator may be used as a pulse 
modulator. 113 A blocking oscillator is a self-excited, overdriven oscillator. During 
the conduction period, the grid is at a high positive potential, causing grid current to 
flow. A biasing potential is developed across a capacitor in the grid circuit by the 
current flow. This potential reaches a value which blocks or stops the conduction 



254 Introduction to Radar Systems 



[Sec. 6.8 



cycle. The blocking oscillator when used for radar modulator application is not really 
an oscillator in the usual sense, but is more a regenerative pulse generator. The 
differences between the regenerative pulse generator and the conventional blocking 
oscillator are discussed in Glasoe and Lebacqz. 98 

One of the limitations of the hard-tube modulator in the past has been the lack of 
vacuum tubes capable of handling the large power required for pulsing big radar 
transmitters. The development of tubes like the RCA types A- 1 5030 and A- 15034 and 
the Machlett ML-7002 shielded-grid triode has made possible the use of hard-tube 
modulators at very high power levels. The ML-7002 operates at 65 kv with a plate 
dissipation of 2 kw and is cooled by immersion in circulating oil. It can switch 3.5 Mw 




Fig. 6.36. Ideal voltage pulse shape for a magnetron modulator. (After Gillette and Oshima, 114 
IRE Trans.) 



of 6-^sec pulse power. 75 The A-l 5030 is capable of switching 22 Mw at a duty factor 
of 0.05 when operated as a hard-tube modulator. 80 In short-pulse application (6 ^sec 
ataprfof 500 cps) the A-l 5034 has been operated at plate voltages up to 55 kv. These 
tubes have been employed as plate modulators for triodes and klystrons. 

Modulator Pulse Shape. 11 * The transmitter pulse shape is not always the same as the 
modulator pulse shape. Figure 6.36 shows the ideal voltage pulse shape for a modulator 
required to pulse a magnetron with a rectangular shape. The initial rise (t — /j) of 
the waveform from zero volts to about 60 per cent of the rated magnetron operating 
voltage may be carried out at any convenient rate. The rate of rise during the next 
interval of time (f x — t 2 ) must be long enough to permit oscillations to start in the 
desired mode of oscillation, usually the n mode. The voltage rises from 60 per cent to 
about 80 per cent of its rated value during this time. If the voltage were to rise too 
rapidly, there would be too little time for the establishment of the desired oscillation 
mode. The magnetron might start oscillating in an unwanted mode, or else the tube 
might not oscillate at all and an arc might form. Once the oscillations are started in 
the desired mode at a low level, the voltage should be increased to the rated operating 
value very rapidly (f 2 — / 3 ). In order to achieve a rectangular RF envelope the voltage 
should remain as nearly constant as possible over the required pulse duration (7 3 — t 4 ). 
If the top of the pulse were not flat but contained ripples, it would cause frequency 
pushing and broadening of the spectrum. At the end of this interval, the voltage 
should fall as rapidly as possible (? 4 — t 5 ) to about 80 per cent of rated voltage. The 
voltage may then be reduced as rapidly as convenient, but not so rapidly that the 



Radar Transmitters 255 

backswing is excessive. Once the pulse has dropped below zero, it should not recross 
the zero axis until the start of the next pulse, else the tube might oscillate and increase 
the noise level at the receiver or present false targets. 115 

The ideal pulse shape can be only approximated in practice. Special circuits have 
been developed for approximating this shape, but except in systems employing 
extremely short pulses, most modulator problems encountered in practice can be 
solved with properly designed conventional circuits. 114 

Other RF generators may impose different requirements on the modulator. For 
example, the Amplitron does not operate in the n mode as does the magnetron. The 
rate of rise of voltage must not be too slow, else operation may occur in the tt mode 
instead of the desired mode. On the other hand, a tube like the klystron presents no 
similar rise-time restrictions on the modulator. 

Comparison of Magnetron Modulators. 98 ' 100 ' 101 The line-type modulator is simple, 
easy to service, and efficient. It is light in weight and small in size and is particularly 
attractive in those applications where large and heavy packages are undesirable, as in 
airborne radar. The time jitter from pulse to pulse is usually worse with this modulator 
than with other types, and changing the pulse duration requires switching in another 
pulse-forming network. 

The saturable reactor has the advantage of no active elements; consequently its life 
should be long. It is not as flexible as the other modulators, and its pulse shape is more 
difficult to control. 

The hard-tube modulator can change pulse duration, pulse shape, or prf with little 
difficulty. It may also be used to generate groups of pulses, as for beacon interrogation. 
Pulse jitter is usually not bothersome. It is less efficient than the others but it offers the 
systems engineer the greatest flexibility in operation. 

REFERENCES 

1. Collins, G. B. (ed.): "Microwave Magnetrons," MIT Radiation Laboratory Series, vol. 6, 
McGraw-Hill Book Company, Inc., New York, 1948. 

2. Wathen, R. L.: Genesis of a Generator: The Early History of the Magnetron,/. Franklin Inst., 
vol. 255, pp. 271-288, April, 1953. 

3. Boot, H. A. H., and J. T. Randall: The Cavity Magnetron, J. Inst. Elec. Eng., vol. 93, pt. IIIA, 
pp. 928-938, 1946. 

4. Hull, J. F., and A. W. Randals: High-power Interdigital Magnetrons, Proc. IRE, vol. 37, 
pp. 1357-1363, November, 1948. 

5. Coombes, E. A.: Pulsed Properties of Oxide Cathodes, J. Appl. Phys., vol. 17, pp. 647-654, 
August, 1954. 

6. Fisk, J. B., H. F. Hagstrum, and P. L. Hartman: The Magnetron as a Generator of Centimeter 
Waves, Bell. System Tech. J., vol. 25, pp. 167-348, 1946. 

7. Esperson, G. A.: Dispenser Cathode Magnetrons, IRETrans., vol. ED-6, pp. 115-118, January, 
1959. 

8. Okress, E. C: Magnetron Mode Transitions, Advances in Electronics and Electron Physics, 
vol. 8, 1958. Also contains an excellent bibliography on the magnetron. 

9. Millman, S., and A. T. Nordsieck : The Rising Sun Magnetron, /. Appl. Phys., vol. 19, pp. 156- 
165, February, 1948. 

10. Bernstein, M. J., and N. M. Kroll: Magnetron Research at Columbia Radiation Laboratory, 
IRE Trans., vol. MTT-2, pp. 33-37, September, 1954. 

11. Hok, G.: Operating Characteristics of Continuous-wave Magnetrons, chap. 21 in Radio 
Research Laboratory Staff, "Very High Frequency Techniques," vol. I, McGraw-Hill Book 
Company, Inc., New York, 1947. 

12. The Smith chart and its use are described in a number of microwave texts. See, for example, 
G. C. Southworth, "Principles and Applications of Waveguide Transmission," D. Van Nostrand 
Company, Inc., Princeton, N.J., 1950. 

13. Beltz, W. F.: Coupled Cavity Tunes X-band Magnetron, Electronics, vol. 29, pp. 182-183, 
March, 1956. 

14. Smith, L. P., and C. I. Schulman: Frequency Modulation and Control by Electron Beams, 
Proc. IRE, vol. 35, pp. 644-657, July, 1947. 



256 Introduction to Radar Systems 

15. Donal, J. S., Jr.: Modulation of Continuous-wave Magnetrons, Advances in Electronics, vol. 4, 
1952. 

16. Kilgore, G. R„ C. I. Shulman, and J. Kurshan: A Frequency-modulated Magnetron for Super- 
high Frequencies, Proc. IRE, vol. 35, pp. 657-664, July, 1947. 

17. Donal, J. S., Jr., R. R. Bush, C. L. Cuccia, and H. R. Hegbar: A 1-kilowatt Frequency-modu- 
lated Magnetron for 900 Megacycles, Proc. IRE, vol. 35, pp. 664-669, July, 1947. 

18. Peters, P. H., Jr., and D. A. Wilbur: Magnetron Voltage Tuning in the S-band, Proc. Natl. 
Electonics Con/. (Chicago), vol. 11, pp. 368-378, 1955. 

19. Welch, H. W., Jr.: Prediction of Traveling-wave Magnetron Frequency Characteristics, 
Frequency Pushing and Voltage Tuning, Proc. IRE, vol. 41, pp. 1631-1653, November, 1953. 

20. Boyd, J. A.: The Mitron: An Interdigital Voltage-tunable Magnetron, Proc. IRE, vol. 43, 
pp. 332-338, March, 1955. 

21 . Bristol, T. R., and G. J. Griffin, Jr. : Voltage-tuned Magnetron for FM Application, Electronics, 
vol. 30, pp. 162-163, May, 1957. 

22. Singh, A., and R. A. Rao: A Proposed Ferrite-tuned Magnetron, /. Inst. Telecommun. Engrs. 
India, vol. 5, pp. 72-76, March, 1959. 

23. Edson, W. A. : "Vacuum-tube Oscillators," chap. 18, John Wiley & Sons, Inc., New York, 1953. 

24. Pritchard, W. L. : Long-line Effect and Pulsed Magnetrons, IRE Trans., vol. MTT-4, pp. 97-1 10, 
April, 1956. 

25. Hull, J. F., G. Novick, and R. Cordray: How Long-line Effect Impairs Tunable Radar, 
Electronics, vol. 27, pp. 168-173, February, 1954. 

26. Boot, H. A. H., H. Foster, and S. A. Self: A New Design of High-power S-band Magnetron, 
Proc. IEE, vol. 105, pt. B, suppl. 10, pp. 419-425, 1958 (Paper 2637 R). 

27. Okress, E. C, C. H. Gleason, R. A. White, and W. R. Hayter: Design and Performance of a 
High Power Pulsed Magnetron, IRE Trans., vol. ED-4, pp. 161-171, April, 1957. (Additional 
data obtained via private communication.) 

28. Technical Information for the Type RK6410/QK338 Magnetron, 3496-9-55, Raytheon Manu- 
facturing Company, Waltham, Mass. (Additional data obtained via private communica- 
tion.) 

29. English Electric Valve Co., Ltd. Technical Publication on Magnetron 7182(M543), December, 
1958. 

30. Beltz, W. F., and R. W. Kissinger: A Long-life C-band Magnetron for Weather Radar Applica- 
tions, Proc. Natl. Electronics Conf. (Chicago), vol. 11, pp. 361-367, 1955. 

31. Brochure on the VF10 Magnetron, List ES/V/3, June, 1957, Ferranti Electric, Inc., New York. 
(Additional data obtained via private communication.) 

32. Dix, C. H., and W. E. Willshaw: Microwave Valves: A Survey of Evolution, Principles of 
Operation, and Basic Characteristics, /. Brit. IRE, vol. 20, pp. 577-609, August, 1960. 

33. Learned, V., and C. Veronda: Recent Developments in High-power Klystron Amplifiers, 
Proc. IRE, vol. 40, pp. 465-469, April, 1952. 

34. Beck, A. H. W., and P. E. Deering: A Three-cavity L-band Pulsed Klystron Amplifier, Proc. 
IEE, vol. 105, pt. B, suppl. 12, pp. 833-838, 1958 (Paper 2659 R). 

35. Swanson, J. P.: Modulator Techniques for Gridded Klystrons and Traveling Wave Tubes, 
Microwave J., vol. 2, no. 7, pp. 29-33, July, 1959. 

36. Preist, D. H. : The Generation of Shaped Pulses using Microwave Klystrons, IRE Natl. Conv. 
Record, pt. 3, pp. 106-113, 1958. 

37. Varian, R. H., and S. F. Varian: A High Frequency Oscillator and Amplifier, /. Appl. Phys., 
vol. 10, pp. 321-327, May, 1939. 

38. Chodorow, M., E. L. Ginzton, I. R. Neilson, and S. Sonkin: Design and Performance of a 
High-power Pulsed Klystron, Proc. IRE, vol. 41, pp. 1584-1602, November, 1953. 

39. Shepherd, J. E.: Harnessing the Electron, Sperry Eng. Rev., vol. 10, pp. 2-18, March-April, 

40. Dalman, G. C. : Developments in Broadband and High-power Klystrons, Proc. Symposium on 
Modern Advances in Microwave Techniques, pp. 123-132, November, 1954, Polytechnic Institute 
of Brooklyn, New York. 

41. Chodorow, M., E. L. Ginzton, J. Jasberg, J. V. Lebacqz, and H. J. Shaw: Development of 
High-power Pulsed Klystrons for Practical Applications, Proc. IRE, vol. 47, pp. 20-29, January, 

42. Speaks, F. A., and D. H. Preist: Super-power Klystrons for UHF Pulse Applications (brochure), 
Eitel-McCullough, Inc., San Bruno, Calif. 

43. Swearingen, J. D., and C. M. Veronda: The SAL-89, A Grid Controlled Pulsed Klystron 
Amplifier, IRE WESCON Conv. Record, vol. 1, pt. 3, pp. 115-121, 1957. 

44. Personal communication from C. M. Veronda of the Sperry Gyroscope Company, Gainesville, 
Fla. 

45. Norris, V. J.: Multi-cavity Klystrons, Electronic Eng., vol. 30, pp. 321-323, May, 1958. 



Radar Transmitters 257 

46. Kreuchen, K. H., B. A. Auld, and N. E. Dixon: A Study of the Broad-band Frequency Response 
of the Multicavity Klystron Amplifier, /. Electronics, vol. 2, pp. 529-567, May, 1957. 

47 Dodds, W. J., T. Moreno, and W. J. McBride, Jr.: Methods of Increasing Bandwidth of 
High Power Microwave Amplifiers, IRE WESCON Conv. Record, vol. 1, pt. 3, pp. 101-110, 

1957 

48. Beaver, W. L., R. L. Jepsen, and R: L. Walter: Wide Band Klystron Amplifiers, IRE WESCON 
Conv. Record, vol. 1, pt. 3, pp. 111-114, 1957. , „ , ■ • 

49. Yadavalli, S. V.: Effect of Beam Coupling Coefficient on Brc>ad-band Operation of Multicavity 
Klystrons', Proc. IRE, vol. 46, pp. 1957-1958, December, 1958. 

50 King, P. G. R.: A 5% Bandwidth 2.5 MW S-band Klystron, Proc. IEE, vol. 105, pt. B, 
suppl. 12, pp. 813-820, 1958 (Paper 2624 R). 

51. Beaver, wf, G. Caryotakis, A. Staprans, and R. Symons: Wide Band High Power Klystrons, 
IRE WESCON Conv. Record, vol. 3, pt. 3, pp. 103-111, 1959. 

52. Pierce, J. R.: Some Recent Advances in Microwave Tubes, Proc. IRE, vol. 42, pp. 1735-1747, 
December, 1954. 

53. Personal communication from T. Moreno of Varian Associates, Palo Alto, Calit. 

54. Dain, J.: Ultra-high-frequency Power Amplifiers, Proc. IEE, vol. 105, pt. B, pp. 513-522, 
November, 1958. . ^ T T , n „ 

55 Pierce, J. R.: "Traveling Wave Tubes," D. VanNostrand Company, Inc., Princeton, N.J., 1950. 
56^ Chodorow, M., and E. J. Nalos: The Design of High-power Traveling-wave Tubes, Proc. IRE, 

vol. 44, pp. 649-659, May, 1956. . . 

57 Chodorow M , E. J. Nalos, S. P. Otsuka, and R. H. Pantell: The Design and Characteristics of a 

Megawatt Space-harmonic Traveling Wave Tube, IRE. Trans., vol. ED-6, pp. 48-53, January, 

1959. 

58. Doehler, O.: Traveling- wave Tubes, Proc. Symposium on Electronic Waveguides, pp. 1-19, 
April, 1958, Polytechnic Institute of Brooklyn, New York. 

59. Nalos, E. J.: Present State of Art in High Power Traveling-wave Tubes, Microwave J., vol. 2, 
no. 12, pp. 31-38, December, 1959. 

60. Brown, W. C. : Description and Operating Characteristics of the Platinotron : A New Microwave 
Tube Device, Proc. IRE, vol. 45, pp. 1209-1222, September, 1957. 

61. Brown, W. C: Platinotron Increases Search Radar Range, Electronics, vol. 30, no. 8, pp. 
164-168, Aug. 1, 1957. rnr , xr 

62. Weil, T. A. : Applying the Amplitron and Stabilitron to MTI Radar Systems, IRE Natl. Conv. 
Record, vol. 6, pt. 5, pp. 120-130, 1958. 

63. Feinstein, J., and G. S. Kino: The Large Signal Behavior of Crossed-field Traveling-wave 
Devices, Proc. IRE, vol. 45, pp. 1364-1373, October, 1957. 

64. Smith, W. A., and F. Zawada: A 3-megawatt, 15-kilowatt S-band Amplitron, Microwave J., 
vol. 2, pp. 42-45, October, 1959. 

65. Dombrowski, G. E.: Theory of the Amplitron, IRE Trans., vol. ED-6, pp. 419-428, October, 

1959 

66. Brown, W. C: Crossed-field Microwave Tubes, Electronics, vol. 33, no. 18, pp. 75-79, Apr. 29, 

67 Doehler, O., A. Dubois, and D. Maillart: An M-type Pulsed Amplifier, Proc. IEE, vol. 106, 
pt. B, suppl. 10, pp. 454^157, 1958. 

68 Wiehtman, B. A. : An Investigation of the Magnetron Amplifier, Stanford Electronics Lab. 
Tech Rept 52 (Project 207), Feb. 9, 1959, ONR Contract Nonr 225(24), NR 373 360. 

69. Warnecke, R. R., W. Kleen, A. Lerbs, O. Dohler, and H. Huber: The Magnetron-type Traveling- 
wave Amplifier Tube, Proc. IRE, vol. 38, pp. 486^95, May, 1950. 
70 Brown W C: U.S. Patent 2,881,270 entitled "Regenerative Amplifier," Apr. 7, 1959. 

71. Brown, W. C, and G. Perloff: High Power CW X-band Amplitron, IRE Intern. Conv. Record, 
' vol. 8,'pt. 3, pp. 52-55, 1960. 

72. Guerlac, H. E. : "OSRD Long History," vol. V, Division 14, "Radar, available from Office ot 
Technical Services, U.S. Department of Commerce. v , ,„„ 

73 Spangenberg, K. R. : "Vacuum Tubes," McGraw-Hill Book Company, Inc., New York, 1948. 

74. Jolly, J. A. : Advantages of Ceramics in Electron Tubes, Proc. Natl. Electronics Conf. {Chicago), 
vol. 13, pp. 999-1008, 1957. 

75. Meacham, D. D.: High-vacuum Power Tubes, Electronics, vol. 33, no. 18, pp. 60-64, Apr. 29, 

76. Dow, W. G.: Transit Time Effects in Ultra-high-frequency Class-C Operation, Proc. IRE, 
vol 35, pp. 35^12, January, 1947. 

77. Groendijk, H.: Microwave Triodes, Proc. IEE, vol. 105, pt. B, suppl. 10, pp. 577-582, 1958 
(Paper 2668 R). r _, 

78. Dain, J.: Factors in the Design of Power Amplifiers for Ultra High Frequency, /. Electronics, 
vol. 1, pp. 35-42, July, 1955. 



258 Introduction to Radar Systems 

79. Sutherland, A. D.: Large Signal Theory of UHF Power Triodes, IRE Trans., vol. ED-6, 
pp. 35-47, January 1959. 

80. Hoover, M. V. : Grid-controlled Power Tubes for Radar Purposes, chap. V in J. Whinnery (ed.), 
"State-of-the-art Report on High Power Pulsed Tubes for Radar Purposes," Advisory Group 
on Electron Tubes report, Contract DA 36-039-SC-74981. 

81. Dow, W. G., and H. W. Welch: The Resnatron, chap. 19 in Radio Research Laboratory Staff, 
"Very High Frequency Techniques," vol. I, McGraw-Hill Book Company, Inc., New York 
1947. r j > 

82. Peterson, F. W.: A New Design Approach for a Compact Kilowatt UHF Beam Power Tube 
IRE WESCON Conv. Record, vol. 2, pt. 3, pp. 36-41, 1958. 

83. Bennett, W. P.: New Beam Power Tubes for UHF Service, IRE Trans., vol ED-3 pp 57-61 
January, 1956. rr ' 

84. Hoover, M. V.: Advances in the Techniques and Applications of Very-high-power Grid- 
controlled Tubes, Proc. IEE, vol. 105, pt. B, suppl. 10, pp. 550-558, May, 1958 (Paper 2752 R). 

85. Bennett, W. P., and H. F. Kazanowski: One-kilowatt Tetrode for UHF Transmitters, Proc. IRE 
vol. 41, pp. 13-19, January, 1953. 

86. Sloan, D. H., and L. C. Marshall: UHF Power, Phys. Rev., vol. 58, p. 193A, 1940. 

87. Salisbury, W. W.: The Resnatron, Electronics, vol. 19, pp. 92-97, February, 1946. 

88. Dow, W. G., and H. W. Welch: The Generation of Ultra-high-frequency Power at the Fifty- 
kilowatt Level, Proc. Natl. Electronics Conf. {Chicago), vol. 2, pp. 603-614, 1946. 

89. McCreary, R. L., W. J. Armstrong, and S. G. McNees: An Axial-flow Resnatron for UHF 
Proc. IRE, vol. 41, pp. 42^16, January, 1953. 

90. Sheppard, G. E., M. Garbuny, and J. R. Hansen: Reflex Resnatron Shows Promise for UHF- 
TV, Electronics, vol. 25, no. 9, pp. 116-119, September, 1952. 

91. Garbuny, M.: Theory of the Reflex Resnatron, Proc. IRE, vol. 41, pp. 37-42, January, 1953. 

92. Tucker, E. B., H. J. Schulte, E. A. Day, and E. E. Lampe: The Resnatron as a 200-MC Power 
Amplifier, Proc. IRE, vol. 46, pp. 1483-1492, August, 1958. 

93. Marshall, L. C, D. H. Sloan, W. J. McBride, Jr., and W. L. Beaver: Resnatron Tubes, Univ. 
California Microwave Lab. Rept., Dec. 15, 1950, under USAF Contracts W-28-099 ac-216 
W-33-038 ac-16649, and W-19-122 ac-38. 

94. Parker, W. N., and M. V. Hoover: Gas Tubes Protect High-power Transmitters, Electronics, 
vol. 29, pp. 144-147, January, 1956. 

95. Brown, G. H., W. C. Morrison, W. L. Behrend, and H. I. Reiskind: Method of Multiple 
Operation of Transmitter Tubes Particularly Adapted for Television Transmission in the Ultra- 
high Frequency Band, RCA Rev., vol. 10, pp. 161-172, June, 1949. 

96. Preist, D. H.: Annular Circuits for VHF and UHF Generators, Proc. IRE, vol. 38 pp 515-520 
May, 1950. vv 

97. Paralleled Amplifiers Increase R-F Power, Electronics, vol. 33, no. 52, pp. 62, 64, Dec. 23, 
1960. 

98. Glasoe, G. N., and J. V. Lebacqz (eds.): "Pulse Generators," MIT Radiation Laboratory Series, 
vol. 5, McGraw-Hill Book Company, Inc., New York, 1948. 

99. Reintjes, J. F., and G. T. Coate: "Principles of Radar," chap. 3, McGraw-Hill Book Company 
Inc., New York, 1952. r J 

100. Zinn, M. H.: A Review of Modulators and Their Requirements, Electronic Design vol 5 
pp. 26-29, Apr. 15, 1957. s ' ' 

101. Zinn, M. H.: Performance and Packaging of Modulators, Electronic Design, vol 5 pp 46^19 
May 15, 1957. ' rr 

102. "Klystron Facts— Case Five." advertising material of Eitel-McCullough, Inc, 1958. 

103. Trinkous, J. W.: Pulse Forming Networks, IRE Trans., vol. CP-3, pp. 63-66, September, 

104. Graydon, A.: The Application of Pulse Forming Networks, Proc. Natl. Electronics Conf. 
(.Chicago), vol. 12, pp. 1071-1086, 1956; also IRE Trans., vol. CP-4, pp. 7-13, March, 1957. 

105. Gray, M. E. : Using Silicon Diodes in Radar Modulators, Electronics, vol. 32, no 24 pp 70-72 
June 12, 1959. ' rr ' 

106. Watrous, W. W., and J. McArtney: Gas Clipper Tubes for Radar Service, Electronics, vol 33 
no. 51, pp. 80-83, Dec. 16, 1960. ' ' 

107. Wittenberg, H. H.: Thyratrons in Radar Modulator Service, RCA Rev., vol. 10, pp 116-133 
March, 1949. ' 

108. Melville, W. S.: The Use of Saturable Reactors as Discharge Devices for Pulse Generators 
Proc. IEE, vol. 98, pt. 3, pp. 185-207, May, 1951. 

109. Mathias, R. A., and E. M. Williams: Economic Design of Saturating Reactor Magnetic Pulsers 
Trans. AIEE, Commun. and Electronics, no. 18, pp. 169-171, March, 1955. 

1 10. Busch, K. J., A. D. Nasley, and C. Neitzert: Magnetic Pulse Modulators, Bell System Tech J 
vol. 34, pp. 943-999, 1955. ' / • > 



Radar Transmitters 259 

111. Thomas, H. E.: Saturable Reactors Fire Radar Magnetrons, Electronics, vol. 31, no. 19, 
pp. 72-75, May 9, 1958. 

112. Kunitz, A.: Using Magnetic Circuits to Pulse Radar Sets, Electronics, vol. 32, no. 27, pp. 42-43, 
July 3, 1959. 

113. Reise, H. A.: "Hard Tube" Pulsers for Radar, Bell Labs. Record, vol. 34, pp. 153-156, April, 
1956. 

114. Gillette, P. R., and K. Oshima: Pulser Component Design for Proper Magnetron Operation, 
IRE Trans., vol. CP-3, pp. 26-31, March, 1956. 

115. Lee, R.: False Echoes in Line-type Radar Pulsers, Proc. IRE, vol. 42, pp. 1288-1295, August, 
1954. 



7 



ANTENNAS 



7.1. Antenna Parameters 1,2 

The purpose of the radar antenna is to act as a transducer between free-space prop- 
agation and guided-wave (transmission-line) propagation. The function of the 
antenna during transmission is to concentrate the radiated energy into a shaped beam 
which points in the desired direction in space. On reception the antenna collects the 
energy contained in the echo signal and delivers it to the receiver. Thus the radar 
antenna is called upon to fulfill reciprocal but related roles. In the radar equation 
derived in Chap. 1 [Eq. (1.8)] these two roles were expressed by the transmitting gain 
and the effective receiving aperture. The two parameters are proportional to one 
another. An antenna with a large effective receiving aperture implies a large trans- 
mitting gain. 

The large apertures required for long-range detection result in narrow beamwidths, 
one of the prime characteristics of radar. Narrow beamwidths are important if 
accurate angular measurements are to be made or if targets close to one another are to 
be resolved. The advantage of microwave frequencies for radar application is that 
apertures of relatively small physical size, but large in terms of wavelengths, can be 
obtained conveniently. High-gain antennas with narrow beamwidths are quite 
practical at microwave frequencies, whereas they would be difficult to achieve at, say, 
short-wave communication frequencies (HF). 

The type of antenna normally used for radar applications differs, in general, from 
antennas used for communications. Radar antennas must generate beams with 
shaped directive patterns which can be scanned. Most communication antennas, on 
the other hand, are usually designed for omnidirectional coverage or for fixed point-to- 
point transmission. The earliest radars that operated in the VHF or the UHF bands 
used array antennas. At the microwave frequencies, the parabolic reflector, which is 
well known in optics, is extensively employed. The vast majority of radar antennas 
have used the parabolic reflector in one form or another. Microwave lenses have also 
found application in radar. In airborne-radar applications, surface-wave antennas 
are sometimes useful when the antenna must not protrude beyond the skin of the air 
frame. 

In this chapter, the radar antenna will be considered either as a transmitting or a 
receiving device, depending on which is more convenient for the particular discussion. 
Results obtained for one may be readily applied to the other because of the reciprocity 
theorem of antenna theory. 1 

Directive Gain. A measure of the ability of an antenna to concentrate energy in a 
particular direction is called the gain. Two different, but related definitions of antenna 
gain are the directive gain and the power gain. The former is sometimes called the 
directivity, while the latter is often simply called the gain. Both definitions are of 
interest to the radar systems engineer. The directive gain is descriptive of the antenna 
pattern, but the power gain is more appropriate for use in the radar equation. 

The directive gain of a transmitting antenna may be defined as 

„ maximum radiation intensity 

g d = jr— : r- 2 - (7.1) 

average radiation intensity 

260 



Sec. 7.1] 



Antennas 261 



where the radiation intensity is the power per unit solid angle radiated in the direction 
(0,<£) and is denoted P(6,<f>). A plot of the radiation intensity as a function of the angular 
coordinates is called a radiation-intensity pattern. The power density, or power per 
unit area, plotted as a function of angle is called a power pattern. The power pattern 
and the radiation-intensity pattern are identical when plotted on a relative basis, that is, 
when the maximum is normalized to a value of unity. When plotted on a relative basis 
both are called the antenna radiation pattern. 

An example of an antenna radiation pattern for a paraboloid antenna is shown 
plotted in Fig. 7.1. 3 The main lobe is at zero degrees. The first irregularity in this 
particular radiation pattern is the vestigial lobe, or "shoulder," on the side of the main 
beam. The vestigial lobe does not always appear in antenna radiation patterns. In 



-10 



1 1 1 I F 

-Main lobe 



t — r 




-10 



80 100 

Degrees off axis 



Fig. 7.1. Radiation pattern for a particular paraboloid reflector antenna illustrating the main-lobe 
and the sidelobe radiation. {After Cutler et al., 3 Proc. IRE.) 

most antennas the first sidelobe appears instead. The first sidelobe is smeared into a 
vestigial lobe as in Fig. 7.1 if the phase distribution across the aperture is not constant. 
Following the first sidelobe are a series of minor lobes which decrease in intensity with 
increasing angular distance from the main lobe. In the vicinity of broadside (in this 
example 100 to 115°), spillover radiation from the feed causes the sidelobe level to rise. 
This is due to energy radiated from the feed which is not intercepted by the reflector. 
Some of it "spills over." The radiation pattern also has a pronounced lobe in the 
backward direction (180°) due to diffraction effects of the reflector and to direct leakage 
through the mesh reflector surface. 

The radiation pattern shown in Fig. 7.1 is plotted as a function of one angular 
coordinate, but the actual pattern is a plot of the radiation intensity P(6,<f>) as a function 
of the two angles 6 and <f>. The two-angle coordinates commonly employed with 
ground-based antennas are azimuth and elevation, but any other convenient set of 
angles can be used. In theoretical work, the classic spherical coordinate system shown 
in Fig. 7.61 is often used. 

A complete three-dimensional plot of the radiation pattern is not always necessary. 
For example, an antenna with a symmetrical pencil-beam pattern can be represented by 
a plot in one angular coordinate. The radiation-intensity pattern for rectangular 
apertures can often be written as the product of the radiation-intensity patterns in the 
two coordinate planes ; for instance, 

P(0,<£) = P(6,Q)P(0& 



262 Introduction to Radar Systems [Sec. 7.1 

and the complete radiation pattern can be specified from the two single-coordinate 
radiation patterns in the 6 plane and the <f> plane. 

Since the average radiation intensity over a solid angle of 4tt radians is equal to the 
total power radiated divided by 4n, the directive gain as defined by Eq. (7 1) can be 
written as 

G = 47r(maximum power radiated/unit solid angle) 

total power radiated ' 

This equation indicates the procedure whereby the directive gain may be found from 
the radiation pattern. The maximum power per unit solid angle is obtained simply by 
inspection, and the total power radiated is found by integrating the volume contained 
under the radiation pattern. Equation (7.2) can be written as 

G 47TP(6>,< ? % ax _4n 

D SSP(d,<f,)d6d4> B (73) 

where B is defined as the beam area : 

B __ SSP(d,<f>) dd d<j> 

iWW (7,4) 

The beam area is the solid angle through which all the radiated power would pass if the 
power per unit solid angle were equal to P(6»,<£) max over the beam area. It defines in 
effect, an equivalent antenna pattern. If 6 B and <f> B are the half-power beamwidths in 
the two orthogonal planes, the beam area B is approximately equal to 0U„ Sub- 
stituting into Eq. (7.3) gives 

g d = r-j- (7.5a) 

if the half-power beamwidths are measured in radians, or 

r 41,253 

if the half-power beamwidths are measured in degrees. 

Power Gain. The definition of directive gain is based primarily on the shape of the 
radiation pattern. It does not take account of losses due to ohmic heating, RF heating 
or a mismatched antenna. The power gain, which will be denoted by G, includes the 
effect of the antenna losses and any other loss which lowers the antenna efficiency. 
The power gain is defined as 

q = maximum radiation intensity from subject ante nna 

radiation intensity from (lossless) isotropic source with same power input "* 
This definition is the one which should be used in the radar equation since it includes 
the losses introduced by the antenna. The directive gain, which is always greater than 
the power gain, is of importance for coverage, accuracy, or resolution considerations 
and is more closely related to the antenna beamwidth. The difference between the two 
antenna gains is usually small. They would be the same if there were no losses 
The power gain and the directive gain may be related by the radiation efficiency factor 
p r as follows : 

G = PrG D (7.7) 

The definitions of power gain and directive gain were described above in terms of a 
transmitting antenna. One of the fundamental theorems of antenna theory concerns 
reciprocity. It states that under certain conditions (usually satisfied in radar practice) 
the transmitting and receiving patterns of an antenna are the same. 1 Thus the gain 
definitions apply equally well whether the antenna is used for transmission or for 



Sec. 7.1] Antennas 263 

reception. The only practical distinction which must be made between transmitting 
and receiving antennas is that the transmitting antenna must be capable of withstanding 
greater power. 

Effective Aperture. Another useful antenna parameter related to the gain is the 
effective receiving aperture, or effective area. It may be regarded as a measure of 
the effective area presented by the antenna to the incident wave. The gain G and 
the effective area A e of a lossless antenna are related by 

= 4ir A e = 4ir Pa A (1 g) 

A 2 A 2 

K = Pa A (7.9) 

where A = wavelength 

A = physical area of antenna 

p a = antenna aperture efficiency (defined in Sec. 7.2) 

Polarization. The direction of polarization of an antenna is defined as the direction 
of the electric field vector. Most radar antennas are linearly polarized ; that is, the 
direction of the electric field vector is either vertical or horizontal. The polarization 
may also be elliptical or circular. Elliptical polarization may be considered as the 
combination of two linearly polarized waves of the same frequency, traveling in the 
same direction, which are perpendicular to each other in space. The relative amplitudes 
of the two waves and the phase relationship between them cart assume any values. If 
the amplitudes of the two waves are equal, and if they are 90° out of (time) phase, the 
polarization is circular. Circular polarization and linear polarization are special 
cases of elliptical polarization. 

Linear polarization is most often used in conventional radar antennas since it is the 
easiest to achieve. The choice between horizontal and vertical linear polarization is 
often left to the discretion of the antenna designer, although the radar systems engineer 
might sometimes want to specify one or the other, depending upon the importance of 
ground reflections. Circular polarization is often desirable in radars which must "see" 
through weather disturbances. 

Sidelobes and Spurious Radiation. An example of sidelobe radiation from a typical 
antenna was shown in Fig. 7.1 . Low sidelobes are generally desired for radar applica- 
tions. If too large a portion of the radiated energy were contained in the sidelobes, 
there would be a reduction in the main-beam energy, with a consequent lowering of the 
maximum gain. 

No general rule can be given for specifying the optimum sidelobe level. This depends 
upon the application and how difficult it is for the antenna designer to achieve low 
sidelobes. If the sidelobes are too high, strong echo signals can enter the receiver and 
appear as false targets. A high sidelobe level makes jamming of the radar easier. 
Also, the radar is more subject to interference from nearby friendly transmitters. 

Sidelobes of the order of 20 to 30 db below the main beam can be readily achieved 
with practical antennas. With extreme care it might be possible to obtain sidelobes as 
low as 35 or 40 db. However, considerably lower sidelobes seem difficult to achieve, 
although there is no theoretical reason why they should not be possible. In many 
applications the radar systems engineer might desire sidelobes of extremely low level, 
but the specifications to the antenna designer must often be dictated by the practical 
limitations imposed by nature and not by the unattainable specifications of theory 
divorced from practice. 

Outline of Chapter. The purpose of this chapter is to summarize the results of 
antenna theory and technology which might be of particular interest in the study and 
practice of radar systems engineering. In the next section, the relationship between 
the radiation pattern (beamwidth, sidelobes, etc.) and the current distribution across 



264 Introduction to Radar Systems [Sec. 7.2 

the antenna aperture is discussed. This is followed by descriptions of the various 
types of antennas which have been applied to radar, including the parabolic reflector, 
lenses, and arrays. Several methods of pattern synthesis are discussed. The effect on 
the radiation pattern of broadband signals and of errors in the aperture distribution is 
considered. The chapter closes with brief discussions of radomes and focused antennas. 

7.2. Antenna Radiation Pattern and Aperture Distribution 

The electric field intensity £(<£) produced by the radiation emitted from the antenna 
is a function of the amplitude and the phase of the current distribution across the 
aperture. 1 - 4 E((f>) may be found by adding vectorially the contribution from the vari- 
ous current elements constituting the aperture. The mathematical summation of all 
the contributions from the current elements contained within the aperture gives the 
field intensity in terms of an integral. This integral cannot be readily evaluated in the 
general case. However, approximations to the solution may be had by dividing the 
area about the antenna aperture into three regions as determined by the mathematical 
approximations that must be made. The demarcations among these three regions are 
not sharp and blend one into the other. 

The region in the immediate neighborhood of the aperture is the near field. It 
extends several antenna diameters from the aperture and, for this reason, is usually of 
little importance to the radar engineer. 

The near field is followed by the Fresnel region. In the Fresnel region, rays from the 
radiating aperture to the observation point (or target) are not parallel and the antenna 
radiation pattern is not constant with distance. Little application is made of the 
Fresnel region in radar. 

The farthest region from the aperture is the Fraunhofer, or far-field, region. In the 
Fraunhofer region, the radiating source and the observation point are at a sufficiently 
large distance from each other so that the rays originating from the aperture may be 
considered parallel to one another at the target (observation point). The vast 
majority of radar antennas are operated in the Fraunhofer region. 

The "boundary" R F between Fresnel and Fraunhofer regions is usually taken to be 
either R F = D 2 /A or the distance R F = ID^jX, where D is the size of the aperture and 
X is the wavelength, D and I being measured in the same units. At a distance given by 
D 2 jX, the gain of a uniformly illuminated antenna is 0.94 that of the Fraunhofer gain at 
infinity. At a distance of 2D 2 /X, the gain is 0.99 that at infinity. 

The plot of the electric field intensity \E(0,</>)\ is called the field-intensity pattern of the 
antenna. The plot of the square of the field intensity \E(Q,<j>)\ 2 is the power radiation 
pattern P(d,(f>), defined in the previous section. 

In the Fraunhofer region, the integral for electric field intensity in terms of current 
distribution across the aperture is given by a Fourier transform relation. Consider the 
rectangular aperture and coordinate system shown in Fig. 7.2. The width of the 
aperture in the z dimension is a, and the angle in the yz plane as measured from the y 
axis is <j>. The far-field electric field intensity, assuming a > I, is 

£(«£) = ( " A(z) exp ()2n - sin </> ) dz (7. 10) 

J -a/2 \ 2. I 

where A{z) = current at distance z, assumed to be flowing in x direction. A(z), the 

aperture distribution, may be written as a complex quantity, including both the 
amplitude and phase distributions, or 

A(z) = \A(z)\ exp/F(z) (7.11) 

where \A(z)\ = amplitude distribution 
T(z) = phase distribution 



Sec. 7.2] Antennas 265 

Equation (7.10) represents the summation, or integration, of the individual contri- 
butions from the current distribution across the aperture according to Huygens' 
principle. At an angle <f>, the contribution from a particular point on the aperture will 
be advanced or retarded in phase by 2ir(zjX) sin <j> radians. Each of these contributions 
is weighed by the factor A(z). The field intensity is the integral of these individual 
contributions across the face of the aperture. 

The aperture distribution has been defined in terms of the current / . It may also be 
defined in terms of the magnetic field component H z for polarization in the x direction, 
or in terms of the electric field component E z for polarization in the z direction, provided 
these field components are confined to the aperture. 5 




£W 



*■/ 



Fig. 7.2. Rectangular aperture and coordinate system for illustrating the relationship between the 
aperture distribution and the far-field electric-field-intensity pattern. 

The expression for the electric field intensity [Eq. (7.10)] is mathematically similar to 
the inverse Fourier transform. Therefore the theory of Fourier transforms can be 
applied to the calculation of the radiation or field-intensity patterns if the aperture 
distribution is known. The Fourier transform of a function /(f) is defined as 



*"(/) = P /(0 ex P (-JW0 dt 

J — 00 

and the inverse Fourier transform is 



/(0 



-\: 



F(f)exp(j2irfi)df 



(7.12) 



(7.13) 



The limits of Eq. (7.10) can be extended over the infinite interval from -co to +oo 
since the aperture distribution is zero beyond z = ±a/2. 

The Fourier transform permits the aperture distribution A{z) to be found for a given 
field-intensity pattern E(</>), since 

A(z) = - f " E(<f>) exp t-j2n - sin <f>) d(sin <j>) (7.14) 

This may be used as a basis for synthesizing an antenna pattern, that is, finding the 
aperture distribution A{z) which yields a desired antenna pattern E(<f>). 

In the remainder of this section, the antenna radiation pattern will be computed for 
various one-dimensional aperture distributions using Eq. (7.10). It will be assumed 
that the phase distribution across the aperture is constant and only the effects of the 
amplitude distribution need be considered. 



266 



Introduction to Radar Systems 



[Sec. 7.2 



The inverse Fourier transform gives the electric field intensity when the phase and 
amplitude of the distribution across the aperture are known. The aperture is defined 
as the projection of the antenna on a plane perpendicular to the direction of propa- 
gation. It does not matter whether the distribution is produced by a reflector antenna, 
a lens, or an array. 

One-dimensional Aperture Distribution. Perhaps the simplest aperture distribution 
to conceive (but not necessarily the easiest to obtain) is the uniform, or rectangular, 
distribution. The uniform distribution is constant over the aperture extending from 
— a/2 to +a/2 and zero outside. For present purposes it will be assumed that the 




-477- 



-377- 



-277- 



77- la A) sin <l> 



Fig. 7.3. The solid curve is the antenna radiation pattern produced by a uniform aperture distri- 
bution ; the dashed curve represents the antenna radiation pattern of an aperture distribution propor- 
tional to the cosine function. 



aperture extends in one dimension only. This might represent the distribution across a 
line source or the distribution in one plane of a rectangular aperture. If the constant 
value of the aperture distribution is equal to A and if the phase distribution across the 
aperture is constant, the antenna pattern as computed from Eq. (7.10) is 



f a/2 / z \ 

E(<f>) = A exp 1 277 - sin <j> I 

J -a/2 V A / 



dz 



£(</>) = 



(7.15) 



(7.16) 



_ A sin [7r(a/A) sin </>]_. [sin ir(ajX) sin </>] 

(77-/A) sin (j> Tr{ajX) sin <f>. 

Normalizing to make E(Q) = 1 results in A = I /a; therefore 

sin [Tr(ajX) sin <f\ 

■n(a/X) sin $ 

This pattern, which is of the form (sin x)jx, is shown by the solid curve in Fig. 7.3. 
The intensity of the first sidelobe is 13.2 db below that of the peak. The angular 
distance between the nulls adjacent to the peak is Xja radians, and the beamwidth as 
measured between the half-power points is 0.88/l/a radians, or S\Xja deg. The wider 
the aperture, the narrower the beamwidth. The voltage pattern of Eq. (7.16) is 
positive over the entire main lobe, but changes sign in passing through the first zero, 
returning to a positive value in passing through the second zero, and so on. The 



Antennas 



267 



Sec. 7.2] 

odd-numbered sidelobes are therefore out of phase with the main lobe, and the even- 
numbered ones are in phase. Such phase reversals are characteristic of antenna 
patterns in which the minima are equal to zero. 1 Also shown in Fig. 7. 3 is the radiation 
pattern for the cosine aperture distribution 



A(z) = 
The normalized radiation pattern is 



77Z 

cos — 
a 



\z\< 



E(<f>) = - 

77 



+ 



sin (w — 



(7.17) 



sin {f + tt/2) 
y) + 77/2 
where y = Tr{ajX) sin </>. 
Table 7.1 lists some of the properties of the radiation patterns produced by various 



. (V - W2) "| 
ip — 7r/2 J 



Table 7.1. Radiation-pattern Characteristics Produced by Various Aperture Distributions f 

A = wavelength ; a = aperture width 



Type of distribution, \z\ < 1 



Uniform; A(z) = 1 

Cosine; A(z) = cos" Oz/2): 

n = 

n = 1 

n = 2 

n = 3 

n = 4 

Parabolic; A{z) = 1- (1 - A)z 2 : 

A = 1.0 

A = 0.8 

A = 0.5 

A = 

Triangular; A{z) = 1 — |zl 

Circular; A(z) = Vl - z 2 



Relative 
gain 



1 

1 

0.810 

0.667 

0.575 

0.515 

1 

0.994 

0.970 

0.833 

0.75 

0.865 



Half-power 

beamwidth, 

deg 



51 A/a 

51 A/a 
69A/a 
83A/a 
95A/a 
lllA/a 

51 A/a 
53A/a 
56A/a 
66A/a 
73A/a 
58.5A/a 



Intensity of first sidelobe, 
db below maximum intensity 



13.2 

13.2 

23 

32 

40 

48 

13.2 
15.8 
17.1 
20.6 
26.4 
17.6 



t Silver. 1 

aperture distributions. The aperture distributions are those which can be readily 
expressed in analytic form and for which the solution of the inverse Fourier transform 
of Eq. (7. 1 0) can be conveniently carried out. The rectangular, cosine to the nth power, 
triangular, and circular distributions are included. (The pattern of a one-dimensional 
circular distribution is equivalent to that produced by the two-dimensional circular 
aperture with uniform illumination.) Although these may not be the distributions 
employed with practical radar antennas, they serve to illustrate how the aperture 
distribution affects the antenna pattern. More complicated distributions which 
cannot be readily found from available tables of Fourier transforms or which cannot be 
expressed in analytical form may be determined by numerical computation methods or 
machine computation. 

The properties of the antenna radiation patterns listed in Table 7.1 are (1) the relative 
gain produced by the particular antenna aperture distribution compared with the gain 
produced by the uniform aperture distribution, (2) the beamwidth in degrees as measured 
between the half-power points of the antenna pattern, and (3) the intensity of the first 
sidelobe as compared with the peak intensity. 

An examination of the information presented in this table reveals that the gain of 
the uniform distribution is greater than the gain of any other distribution. It is shown 
by Silver 1 that the uniform distribution is indeed the most efficient aperture distribution, 



268 Introduction to Radar Systems [Sec. 7.2 

that is, the one which maximizes the antenna gain. Therefore the relative-gain column 
may be considered as the efficiency of a particular aperture distribution as compared 
with the uniform, or most efficient, aperture distribution. The relative gain is also 
called the aperture efficiency [Eq. (7.9)]. The aperture efficiency times the physical 
area of the aperture is the effective aperture. 

Another property of the radiation pattern illustrated by Table 7. 1 is that the antennas 
with the lowest sidelobes (adjacent to the main beam) are those with aperture distri- 
butions in which the amplitude tapers to a small value at the edges. The greater the 
amplitude taper, the lower the sidelobe level but the less the relative gain and the 
broader the beamwidth. Thus low sidelobes and good efficiency run counter to one 
another. For example, an aperture distribution which follows a cosine-squared law 
has a relatively large illumination taper. Its sidelobe level is 32 db as compared with 
the 13.2 db of the uniform illumination. 

A word of caution should be given concerning the ability to achieve in practice low 
sidelobe levels with extremely tapered illuminations, such as those of cos 3 and cos 4 . 
It was assumed in the computation of these radiation patterns that the distribution of 
the phase across the aperture was constant. In a practical antenna this will not 
necessarily be true since there will always be some unavoidable phase variations caused 
by the inability to fabricate the antenna as desired. Any practical device is never 
perfect; it will always be constructed with some error, albeit small. The phase varia- 
tions due to the unavoidable errors can cause the sidelobe level to be raised and the gain 
to be lowered. There is a practical limit beyond which it becomes increasingly difficult 
to achieve low sidelobes even if a considerable amplitude taper is used. The economic 
limit to the sidelobe level of conventional antennas seems to be of the order of 35 to 
40 db. 

Antenna Efficiency. The aperture efficiency is a measure of the gain of an antenna 
relative to the gain of a similar antenna with uniform aperture distribution. The 
over-all antenna efficiency would be the same as the aperture efficiency if the antenna 
were perfect, that is, if all the energy from the feed were collected without loss by the 
reflector and if there were no losses in the antenna due to mismatch or to other causes. 
In practical antennas, losses are present and the over-all efficiency is the product of 
three factors :(1) the aperture efficiency, (2) the spillover efficiency (if a reflector or lens) 
and (3) the efficiency of the feed. The radiation efficiency defined by Eq. (7.7) is the 
product of the last two factors. 

Circular Aperture. 6 The examples of aperture distribution presented previously in 
this section applied to distributions in one dimension. We shall consider here the 
antenna pattern produced by a two-dimensional distribution across a circular aperture. 
The polar coordinates (r,d) are used to describe the aperture distribution A(r,6), where r 
is the radial distance from the center of the circular aperture, and 6 is the angle measured 
in the plane of the aperture with respect to a reference. Huygens' principle may 
be applied in the far field by dividing the plane wave across the circular aperture 
into a great many spherical wavelets, all of the same phase but of different ampli- 
tude. To find the field intensity at a point a distance 7? from the antenna, the 
amplitudes of all the waves are added at the point, taking account of the proper 
phase relationships due to the difference in path lengths. The field intensity at a 
distance R is thus proportional to 

E(R) =j 2 "dd( r °A(r,d) exp (- — )r dr (7.18) 

where r is the radius of the aperture. For a circular aperture with uniform distribution, 



Sec. 7.3] 



Antennas 



269 



the field intensity is proportional to 

£(<£) = P'dfl pexp (-27r-sin^cosfl)rdr = irrg2J 1 (f)/f (7.19) 



The first sidelobe is 



where f = 277(> /A) sin <j> 

j^) = first-order Bessel function 
A plot of the normalized radiation pattern is shown in Fig. 7.4. 
17.5 db below the main lobe, and the beamwidth is 58.5A/Z). 

The effect of tapering the amplitude distribution of a circular aperture is similar to 
tapering the distribution of a linear aperture. The sidelobes may be reduced, but at 
the expense of broader beamwidth and less antenna gain. One aperture distribution 
which has been considered in the past 1 is [1 — (rjr f] v , where/? = 0, 1, 2, ... . The 



-10 




-2 2 

(, = 2n{r /\) sin 



Fig. 7.4. Radiation pattern for a uniformly illuminated circular aperture. 

radiation pattern is of the form /„ hl (f )/£ p F1 . When/? = 0, the distribution is uniform 
and the radiation pattern reduces to that given above. For p = 1 , the gain is reduced 
75 per cent, the half-power beamwidth is 72.6A/A and the first sidelobe is 24.6 db 
below the maximum. The sidelobe level is 30.6 db down for/? = 2, but the gain 
relative to a uniform distribution is 50 per cent. Additional properties of this 
distribution can be found in Ref. 1 , table 6.2. 

Aperture Blocking. An obstacle in front of the aperture can cause an unavoidable 
blocking or shadowing and alter the effective aperture distribution. One of the chief 
examples of aperture blocking is the feed in reflector-type antennas. Aperture 
blocking degrades the performance of an antenna by lowering the gain and raising the 
sidelobes. The effect of aperture blocking can be approximated by subtracting the 
radiation pattern produced by the obstacle from the radiation pattern of the undisturbed 
aperture. This procedure is possible because of the linearity of the Fourier-transform 
relationship. An example of the effect of aperture blocking caused by the feed in a 
paraboloid-reflector antenna is shown in Fig. 7.5. 7 

7.3. Parabolic-reflector Antennas 1 7S 

One of the most widely used microwave antennas is the parabolic reflector (Fig. 7.6). 
The parabola is illuminated by a source of energy called the feed, placed at the focus of 



270 Introduction to Radar Systems [Sec. 7.3 

the parabola and directed toward the reflector surface. The parabola is well suited for 
microwave antennas because (1) any ray from the focus is reflected in a direction 
parallel to the axis of the parabola and (2) the distance traveled by any ray from the 
focus to the parabola and by reflection to a plane perpendicular to the parabola axis is 
independent of its path. Therefore a point source of energy located at the focus is 
converted into a plane wavefront of uniform phase. 



-20 




-5 5 

grees off axis 



Fig. 7.5. Effect of aperture blocking caused by the feed in a parabolic-reflector antenna. (From C. 
Cutler," Proc. IRE.) 



The basic parabolic contour has been used in a variety of configurations. Rotating 
the parabolic curve shown in Fig. 7.6 about its axis produces a parabola of revolution 
called a circular parabola, or a paraboloid. When properly illuminated by a point 
source at the focus, the paraboloid generates a nearly symmetrical pencil-beam-antenna 
pattern. Its chief application has been for tracking-radar antennas. Examples of 
the paraboloid are shown in Figs. 5.19 to 5.21. 

An asymmetrical beam shape can be ob- 
tained by using only a part of the parab- 
oloid. This type of antenna, an example 
of which is shown in Fig. 1.6, is widely used 
when fan beams are desired. 

Another means of producing either a sym- 
metrical or an asymmetrical antenna pattern 
is with the parabolic cylinder. 1 > 5 > 9 The para- 
bolic cylinder (Fig. 1.11) is generated by 
moving the parabolic contour parallel to itself. 
A line source such as a linear array, rather 
than a point source, must be used to feed the 
parabolic cylinder. The beamwidth in the 
plane containing the linear feed is determined 
by the illumination of the line source, while 
the beamwidth in the perpendicular plane is determined by the illumination across the 
parabolic profile. The reflector is made longer than the linear feed to avoid spillover 
and diffraction effects. One of the advantages of the parabolic cylinder is that it can 
readily generate an asymmetrical fan beam with a much larger aspect ratio (length to 
width) than can a section of a paraboloid. It is not practical to use a paraboloidal 
reflector with a single horn feed for aspect ratios greater than about 8:1, although it is 
practical to use the parabolic cylinder for aspect ratios of this magnitude or larger. 




Vertex 

or 
apex 



Fig. 7.6. Parabolic-reflector antenna. 



Sec. 7.3] Antennas 271 

Still another variation of the parabola is the parabolic torus shown in Fig. 7.17 and 
discussed in Sec. 7.4. It is generated by moving the parabolic contour over an arc of a 
circle whose center is on the axis of the parabola. It is useful where a scan angle less 
than 1 20° is required and where it is not convenient to scan the reflector itself. Scanning 
is accomplished in the parabolic torus by moving the feed. 

There are other variations of parabolic reflectors such as cheeses, pillboxes, and 
hoghorns, descriptions of which may be found in the literature. 1 - 5 

Feeds for Paraboloids }^ The ideal feed for a paraboloid consists of a point source 
of illumination with a pattern of proper shape to achieve the desired aperture distri- 
bution. It is important in a paraboloid that the phase of the radiation emitted by the 
feed be independent of the angle. The radiation pattern produced by the feed is 
called the primary pattern; the radiation pattern of the aperture when illuminated by 
the feed is called the secondary pattern. 

Practical feeds for paraboloids only approximate the ideal. The early paraboloids 
were generally fed by the simple half-wave-dipole element. The half- wave dipole, as a 
feed for a paraboloid, suffers from two major limitations. First, the dipole radiates 
uniformly in a plane perpendicular to its length and radiates no energy in the direction 
of its length. The resulting radiation pattern is therefore doughnut-shaped. If the 
paraboloid reflector subtends a solid angle of 180° at the focus (a rather large angle), 
half of the energy radiated by the dipole would be radiated into space without striking 
the reflector. With small paraboloids (apertures of a few square wavelengths), it is 
possible to phase the rearward primary energy to reinforce the secondary energy from 
the paraboloid reflector in order that the rearward energy contribute to the gain of the 
antenna and not be lost. However, for large antennas most of the energy not striking 
the reflector is wasted. 

The efficiency of the simple dipole feed can be increased with a more elaborate feed 
which directs most of the energy radiated by the feed in the direction of the reflector. 
This is accomplished by a parasitically excited reflector element placed behind the 
dipole to reflect energy toward the paraboloid. The parasitic reflector can be another 
dipole, a plane sheet, a half cylinder, or a hemisphere. 

The second shortcoming of the dipole as a paraboloid feed is its poor polarization 
characteristic. In an ideal feed all the energy reflected from the paraboloid surface is 
polarized in the same direction. If it is not, the energy polarized at some other direc- 
tion is wasted because the antenna might not be designed to respond to a different 
polarization. The dipole feed causes some of the reflected energy to be perpendicular 
to that of the primary radiation. This cross-polarized radiation causes an effective 
reduction of the antenna gain and results in the generation of sidelobes with polariza- 
tion orthogonal to the primary polarization. The extent of the cross-polarized energy 
depends upon the shape of the dish. It is minimized with a shallow reflector, that is, 
one with a large ratio of focal length to diameter. 

A better feed than the half-wave dipole is the open-ended waveguide. Most of the 
energy is directed in the forward direction, and the phase characteristic is usually good, 
if radiating in the proper mode. A circular paraboloid might be fed by a circular, 
open-ended waveguide operating in the TE U mode. A rectangular guide operating in 
the TE 10 mode does not give a circularly symmetric radiation pattern since the dimen- 
sions in the E and H planes, as well as the current distributions in these two planes, are 
different. As this is generally true of most waveguide feeds, a perfectly symmetrical 
antenna pattern is difficult to achieve in practice. The rectangular guide may be used, 
however, for feeding an asymmetrical section of a paraboloid that generates a fan beam 
wider in the H plane than in the E plane. 

When more directivity is required than can be obtained with a simple open-ended 
waveguide, some form of waveguide horn may be used. The waveguide horn is 
probably the most popular method of feeding a paraboloid for radar application. 



272 Introduction to Radar Systems 



[Sec. 7.3 



Optimum Feed Illumination Angle. If the radiation pattern of the feed is known, the 
illumination of the aperture can be determined and the resulting secondary beam 
pattern can be found by evaluating a Fourier integral or performing a numerical 
calculation. The radiation pattern of a 0.84A-diameter circular waveguide is shown in 
Fig. 7.7. If one wished to obtain relatively uniform illumination across a paraboloid 



-5 


1 1 1 1^- 


F-nI i i i 


-10 


- / 


\ - 


-15 


- / 


\ - 


?o 


/ \ 1 1 1 


1 i i i i\ 



-100 -80 -60 -40 -20 20 40 
6 degrees off axis 



60 80 100 



Fig. 7.7. Radiation pattern of 0.84A-diameter circular-waveguide aperture. {From C. Cutler,'' Proc. 
IRE.) 



100 



aperture with a feed of this type, only a small angular portion of the pattern should be 
used. An antenna with a large ratio of focal distance to antenna diameter would be 
necessary to achieve a relatively uniform illumination across the aperture. Also, a 
significant portion of the energy radiated by the feed would not intercept the paraboloid 
and would be lost. The lost "spillover" energy results in a lowering of the over-all 

efficiency and defeats the purpose of the 
uniform illumination (maximum aperture 
efficiency). On the other hand, if the angle 
subtended by the paraboloid at the focus is 
large, more of the radiation from the feed will 
be intercepted by the reflector. The less the 
spillover, the higher the efficiency. However, 
the illumination is more tapered, causing a 
reduction in the aperture efficiency. There- 
fore, there will be some angle at which these 
two counteracting effects result in maximum 
efficiency. This is illustrated in Fig. 7.8 for 
the circular-waveguide feed whose pattern is 
shown in Fig. 7.7. The maximum of the 
curve is relatively broad, so that the optimum 
angle subtended by the antenna at the focus 
is not critical. The greatest efficiency is ob- 
tained with a reflector in which the radiation 
from the feed in the direction of the edges is 
between 8 and 12 db below that at the center. 
As a rough rule of thumb, the intensity of the energy radiated toward the edge of the 
reflector should usually be about one-tenth the maximum intensity. The aperture dis- 
tribution at the edges will be even less than one-tenth the maximum because of the 
longer path from the feed to the edge of the reflector than from the feed to the center 
of the dish. When the primary feed pattern is 10 db down at the edges, the first minor 
lobe in the secondary pattern is in the vicinity of 22 to 25 db. 




20 40 60 80 100 

Half angle subtended by paraboloid at focus 

Fig. 7.8. Efficiency of a paraboloid as a 
function of the half angle subtended by the 
paraboloid at the focus. (From C. Cutler, 7 
Proc. IRE.) 



Sec. 7.3] Antennas 273 

Calculations of the antenna efficiency based on the aperture distribution set up by the 
primary pattern as well as the spillover indicate theoretical efficiencies of about 80 per 
cent for paraboloidal antennas when compared with an ideal, uniformly illuminated 
aperture In practice, phase variations across the aperture, poor polarization charac- 
teristics, and antenna mismatch reduce the efficiency to the order of 55 to 65 per cent 
for ordinary paraboloidal-reflector antennas. 

Feed Support. The resonant half-wave dipole and the waveguide horn can be 
arranged to feed the paraboloid as shown in Fig. 7.9a and b. These two arrangements 
are examples of rear feeds. The waveguide rear feed shown in Fig. 1.9b produces an 
asymmetrical pattern since the transmission line is not in the center of the dish. A rear 
feed not shown in Fig. 7.9 is the Cutler feed, 7 a dual-aperture rear feed in which the 
waveguide is in the center of the dish and the energy is made to bend 1 80 at the end ot 






^=^ 



[a] (b) (c) 

Fig. 7.9. Examples of the placement of the feeds in parabolic reflectors, (a) Rear feed using half-wave 
dipole; {b) rear feed using horn ; (c) front feed using horn. 

the waveguide by a properly designed reflecting plate. The rear feed has the advantage 
of compactness and utilizes a minimum length of transmission line. 

The antenna may also be fed in the manner shown in Fig. 7.9c. This is an example 
of a front feed. It is well suited for supporting horn feeds, but it obstructs the aperture. 

Two basic limitations to any of the feed configurations mentioned above are aperture 
blocking and impedance mismatch in the feed. The feed, transmission line, and sup- 
porting structure intercept a portion of the radiated energy and alter the effective 
antenna pattern. Some of the energy reflected by the paraboloid enters the feed and 
acts as any other wave traveling in the reverse direction in the transmission line. 
Standing waves are produced along the line, causing an impedance mismatch and 
a degradation of the transmitter performance. The mismatch can be corrected by 
an impedance-matching device, but this remedy is effective only over a relatively 
narrow frequency band. Another technique for reducing the effect of the reflected 
radiation intercepted by the feed is to raise a portion of the reflecting surface at 
the center (apex) of the paraboloid. The raised surface is made of such a size and 
distance from the original reflector contour as to produce at the focus a reflected 
signal equal in amplitude but opposite in phase to the signal reflected from the 
remainder of the reflector. The two reflected signals cancel at the feed, so that there 
is no mismatch. The raised portion of the reflector is called an apex-matching 
plate Although the apex-matching plate has a broader bandwidth than matching 
devices inside the transmission line, it causes a slight reduction in the gain and in- 
creases the minor-lobe level of the radiation pattern. 

Offset Feed 1 < 1 Both the aperture blocking and the mismatch at the feed are elimi- 
nated with the offset-feed parabolic antenna shown in Fig. 7.10. The center of the feed 
is placed at the focus of the parabola, but the horn is tipped with respect to the parabola s 
axis The major portion of the lower half of the parabola is removed, leaving that 
portion shown by the solid curve in Fig. 7. 10. For all practical purposes the feed is out 



Parabola 



274 Introduction to Radar Systems [Sec. 7.3 

of the path of the reflected energy, so that there is no pattern deterioration due to 

aperture blocking nor is there any significant amount of energy intercepted by the feed 

to produce an impedance mismatch. 

It should be noted that the antenna aperture of an offset parabola (or any parabolic 

reflector) is the area projected on a plane perpendicular to 

its axis and is not the surface area. 

The offset parabola eliminates two of the major limi- 
tations of rear or front feeds. However, it introduces 
problems of its own. Cross-polarization lobes are pro- 
duced by the offset geometry, which may seriously 
deteriorate the radar system performance. 1 Also, it is 
usually more difficult to properly support and to scan an 
offset-feed antenna than a circular paraboloid with rear 
feed. 

f/D Ratio. An important design parameter for reflector 
antennas is the ratio of the focal length / to the antenna 
diameter D, or f/D ratio. The selection of the proper///) 
ratio is based on both mechanical and electrical consider- 
ations. A small f/D ratio requires a deep-dish reflector, 
while a large f/D ratio requires a shallow reflector. The shallow reflector is easier to 
support and move mechanically since its center of gravity is closer to the vertex, but 
the feed must be supported farther from the reflector. The farther from the reflector 
the feed is placed, the narrower must be the primary-pattern beamwidth and the larger 




Fig. 7.10. Parabolic reflector 
with offset feed. 



80 


_ 1 1 1 


1 


1 


1 I 


1—+- 


- 


60 


1 B / / ^ 










- 


40 


J / 










- 


20 


c/ / 










- 


10 
8 


/ d/ 










— 


6 




<^£- 


3 1 \) 


r 




- 


4 


'-I 










- 




1 Somple 


a 


b 


Mesh 


T 


% open 


- 




/ A 


2 V? 


IV. 


IVz" 


V« 


90.8 


Z 


L B 


IV. 


'/« 


V." 


Vs. 


92.5 




C 


1 


V 2 


V 8 " 


Vs. 


87.4 


1 


' D 
I 1 


V. 

1 


V. 
1 


V." 

1 


Vs. 
1 1 


83.8 

1 1 



1.0 



3.0 



5.0 7.0 9.0 
Frequency, Gc 

(a) 



11.0 



100 
80 
60 

40 



0.1 



"i i i i — i — r 



"i — n 




£mesh <0.1% trons 



1.0 



J 1 I l i 



3.0 



J L 



5.0 7.0 9.0 
Frequency , Gc 

Kb) 



11.0 



Fig. 7.11. Per cent transmission through aluminum mesh, (a) Polarization perpendicular to long 
dimension; (6) polarization parallel to long dimension. Table in («) applies to both figures; dimen- 
sions given in inches. {After Ricardi and Devane," courtesy Electronic Industries.) 



Sec. 7.3] 



Antennas 275 



must be the feed. On the other hand, it is difficult to obtain a feed with uniform phase 
over the wide angle necessary to properly illuminate a reflector with small fjD 

Most parabolic-reflector antennas seem to have//Z) ratios ranging from 0.3 to 0.5. 
Antennas used to generate monopulse-tracking beams have///) ratios of 0.5 to 1.0 or 
more in order to obtain the proper crossover level of the multiple beams with ordinary 

waveguide feeds. . . , 

Reflector Surfaces. The reflecting surface may be made of a solid sheet material, but 
it is often preferable to use a wire screen, metal grating, perforated metal, or expanded 
metal mesh The expanded metal mesh made from aluminum is a popular form. A 
nonsolid surface such as a mesh offers low wind resistance, light weight, low cost, ease 
of fabrication and assembly, and the ability to conform to variously shaped reflector 
surfaces. 10 - 11 However, a nonsolid surface may permit energy to leak through, with 
the result that both the backlobe of the antenna 
and the relative intensity of the sidelobes adjacent 
to the main beam will increase and the antenna 
gain will decrease. 

The leakage through several types of mesh 
screens has been measured by Ricardi and 
Devane. 11 The transmission of linear-polarized 
plane waves at normal incidence to a plane sheet 
of expanded aluminum with a diamond mesh is 
shown in Fig. 7.1 la for polarization perpendicu- 
lar to the long dimension and in Fig. 7.116 for 
polarization parallel to the long dimension. The 
dimensions of the sample screens for which the 
results of Fig. 7.1 la and b apply are given by the 
table in Fig. 7.11a. 

The presence of ice on the reflector surface is 
an important consideration for both the electrical 
and the mechanical design of the antenna. Ice 
adds to the weight of the antenna and makes it 
more difficult to rotate. In addition, if the ice 
were to close the holes of a mesh antenna so that 
a solid rather than an open surface is presented to 
the wind, bigger motors would be needed to oper- 
ate the antenna. The structure also would have 
to be stronger. 

The effect of ice on the electrical characteristics 
of a mesh reflecting surface is twofold. 12 On the 
one hand, ice which fills a part of the space be- 
tween the mesh conductors may be considered a dielectric. A dielectric around the 
wires is equivalent to a shortening of the wavelength incident on the mesh. The spacing 
between wires appears wider, electrically, causing the transmission coefficient of the sur- 
face to increase. On the other hand, the total reflecting surface is increased by the pres- 
ence of ice reducing the transmission through the mesh. The relative importance of 
these two effects determines whether there is a net increase or a net decrease in trans- 
mission. In unfavorable cases, even strongly reflecting meshes can lose their reflecting 
properties almost completely. Two examples of transmission through a grid of parallel 
wires coated with ice are shown in Fig. 7.12. These indicate that the percentage trans- 
mission can increase significantly as a result of the dielectric properties of ice. With a 
further increase in the amount of ice, the reflecting properties dominate and the percent- 
age transmission ceases to increase and starts to decrease (not shown in the figure). 



100 


I 


I 


I 1 




90 








- 


80 








- 


70 




(a) 


(b) 




C 

o 










?60 

E 

(/i 

§50 


_ 








3S 










40 


- - 








30 


- 








20 


- 








10 


- 









0.1 



0.2 0.3 0.4 
Radius oi ice, cm 



0.5 0.6 



Fig. 7.12. Per cent transmission through 
a grid of parallel wires coated with ice at 
X band (A = 3.2 cm), (a) Wire diameter 
= 0.02 cm, spacing between wires = 0.5 
cm; (6) wire diameter = 0.1 cm, spacing 
between wires = 1 cm. (After Para- 
monov, 12 Radiotechnikq.) 



276 Introduction to Radar Systems 



[Sec. 7.3 



%" water 
internal 
pressure 



A 


r-inflated tube (lOpsi) 
■—Fabric paraboloid 






Metolized 

\ fabric 
\ paraboloid 


/ / 
/ / 

/ / 
// 

1 1 




1 Feed / 


1 

[ Feed-horn 

i support-^ 



Inner tower 



-Feed horn \ 
I 



Inner tower 



Fig. 7.13. Outline of the Paraballoon antenna. (Courtesy Westinghouse Electric Corporation, 
Electronics Division.) 



Reflector— 



—Stacked -beam 
feedhorn 




Turntable 



Fig. 7.14. Cutaway view of a Paraballoon antenna, inside a radome, for the AN/TPS-27, 3-D tactical 
radar. (Courtesy Westinghouse Electric Corporation, Electronics Division.) 



Sec. 7.4] Antennas 277 

Antennas which might be exposed to icing conditions can be protected by enclosure 
in radomes, as described in Sec. 7.12. 

ParabaUoons 1316 A parabolic reflector somewhat different from that described 
previously is the Paraballoon (Fig. 7.13), an inflatable antenna made from a plastic 
material such as vinyl-coated fiberglass, contoured during initial fabrication into two 
paraboloid-shaped halves. The two paraboloids of plastic material are joined at the 
rims and inflated. A pressure differential of as little as 0.02 psi is sufficient for satis- 
factory operation of a 30-ft-diameter Paraballoon. The early ParabaUoons used as 
the reflector a sheet of Mylar with vapor-deposited aluminum attached to the inside 
surface of one of the paraboloids. A reflecting surface may also be made by imbed- 
ding metallic silver particles inside the plastic coating on the fabric. The plastic 
material of the Paraballoon has little effect on the RF energy. 

The whole Paraballoon structure is enclosed within a protective inflated plastic 
radome Both the radome and the antenna are kept above the surrounding air pressure 
by blowers. Because of the relatively small pressure required to inflate the Para- 
balloon its operation is not affected by moderate leakage or puncture. A 30-ft- 
diameter Paraballoon can operate satisfactorily even if punctured by 50 holes the size 
of 20-mm shells. The advantage claimed for this antenna is that it is readily trans- 
portable and easily erected because of its light weight and small size when deflated. 
Repeated inflation and deflation cycles have little effect on the contour. It is claimed 
that the contour can be maintained to as good a tolerance as conventional metal 
reflectors, sometimes better. 

A 30-ft-diameter oblate Paraballoon is used with the AN/TPS-27 stacked beam 
(3-D) tactical radar (Fig. 7.14), and a 50-ft-diameter Paraballoon is used in the 
AN/TPS-22, a long-range search radar designed for forward tactical areas. The total 
installed weight for the complete antenna system of the AN/TPS-27 including radome 
is approximately 9,000 lb. The complete radar can be erected and in operation in 
about 4 hr. 

7.4. Scanning-feed Reflector Antennas 

Large antennas are sometimes difficult to scan mechanically with as much flexibility 
as one might like. Some technique for scanning the beam of a large antenna must 
often be used other than the brute-force technique of mechanically positioning the 
entire structure. Phased array antennas and lens antennas offer the possibility of 
scanning the beam without the necessity for moving large mechanical masses. These 
are discussed later in this chapter. The present section considers the possibility of 
scanning the beam over a limited angle with a fixed reflector and a movable feed. It is 
much easier to mechanically position the feed than it is to position the entire antenna 
structure. In addition, large fixed reflectors are usually cheaper and easier to manu- 
facture than antennas which must be moved about. 

The beam produced by a simple paraboloid reflector can be scanned over a limited 
angle by positioning the feed. 1 ' 17 - 18 However, the beam cannot be scanned too far 
without encountering serious deterioration of the antenna radiation pattern because 
of increasing coma and astigmatism. The gain of a paraboloid with fjD = 0.25 
(/= focal distance, D = antenna diameter) is reduced to 80 per cent of its maximum 
value when the beam is scanned ±3 beamwidths off axis. A paraboloid with 
fjD = 0.50 can be scanned ±6.5 beamwidths off axis before the gain is reduced to 
80 per cent of maximum (Ref. 1 , p. 488). The antenna impedance also changes with a 
change in feed position. Hence scanning a simple paraboloid antenna by scanning the 
feed is possible, but is generally limited in angle because of the deterioration in the 
antenna pattern after scanning but a few beamwidths off axis. 

Spherical Reflectors. If the paraboloid reflector is replaced by a spherical-reflector 



278 Introduction to Radar Systems [ Sec 7 4 

surface, it is possible to achieve a wide scanning angle because of the symmetry of the 
sphere. However, a simple spherical reflector does not produce an equiphase radiation 
pattern (plane wave), and the pattern is generally poor. The term spherical aberration 
is used to describe the fact that the phase front of the wave radiated by a spherical 
reflector is not plane as it is with a wave radiated by an ideal parabolic reflector There 
are at least three techniques which might be used to minimize the effect of spherical 
aberration. One is to employ a reflector of sufficiently large radius so that the portion 
ot the sphere is a reasonable approximation to a paraboloid. 19 " 21 The second approach 
is to compensate for the spherical aberration with special feeds or correcting lenses 
These techniques yield only slightly larger scan angles than the single paraboloid 
reflector with movable feed. 

A third technique to approximate the spherical surface and minimize the effects of 
spherical aberration is to step a parabolic reflector as shown in Fig. 7 15 8.22,23 The 
focal length is reduced in half-wavelength steps, making a family of confocal parabo- 
loids. It is possible to scan the stepped reflector to slightly wider angles than a 




Generoting 
parabola 



Center of 
sphere 




Fig. 7.15. Stepped parabolic reflector. 



Fig. 7.16. Principle of the parabolic-torus 
antenna. 



simple paraboloid, but not as wide as with some other scanning techniques Dis- 
advantages of this reflector are the scattered radiation from the stepped portions and 
the narrow bandwidth. 

If only a portion of the spherical reflector is illuminated at any one time, much wider 
scan angles are possible than if the entire aperture were illuminated. Li 21 has described 
experiments using a 10-ft-diameter spherical reflector at a frequency of 1 1 2 Gc The 
focal length was 29.5 in. If the phase error from the sphere is to differ from that of a 
paraboloid by no more than A/ 16, the maximum permissible diameter of the illumi- 
nated surface should be 3.56 ft. The beamwidth required of the primary feed pattern 
is determined by the illuminated portion of the aperture. Li used a square-aperture 
horn with diagonal polarization in order to obtain the required primary beamwidth 
and low-primary-pattern sidelobes (better than 25 db). The resulting secondary beam- 
width from the sphere was about 1.8° (39.4 db gain) with a relative sidelobe level of 20 
db. A total useful scan angle of 140° was demonstrated. This type of antenna is 
similar in many respects to the torus antenna described below. 

Parabolic Torus. Wide scan angles can be obtained with a parabolic-torus con- 
Jiguration. The principle of the parabolic-torus antenna is shown in Fig 7 16 

and a photograph of an actual torus antenna used in BMEWS (Ballistic Missile Early 



Sec. 7.4] 



Antennas 279 



Warning System) is shown in Fig. 7.17. The parabolic torus is generated by rotating a 
section of a parabolic arc about an axis parallel to the latus rectum of the parabola. 
The cross section in one plane (the vertical plane in Fig. 7.16) is parabolic, while the 
cross section in the orthogonal plane is circular. The beam angle may be scanned by 
moving the feed along a circle whose radius is approximately half the radius of the torus 
circle The radius of the torus is made large enough so that the portion of the circular 
cross 'section illuminated by the feed will not differ appreciably from the surface of a 
true parabola. Because of the circular symmetry of the reflector surface in the hori- 
zontal plane, the beam can be readily scanned in this plane without any deterioration 
in the pattern. 




Fig. 7.17. Parabolic-torus antenna used in the surveillance radar of the Balhst ,c Miss le ^ Early 
Warning System (BMEWS). (Crane to left of figure is part of the erect ion eqinp ment, not the an enna.) 
This antenna is 165 ft high and 400 ft wide and uses 1 ,500 tons of steel. {Courtesy General Ekctnc Co., 
Heavy Military Electronics Department) 

The wave reflected from the surface of the parabolic torus is not perfectly plane, but 
it can be made to approach a plane wave by proper choice of the ratio ^of focal lengthy 
to the radius of the torus R. The optimum ratio of///? lies between 0.43 ^and .0.45 

Good radiation patterns are possible in the principal planes with sidelobes only 
slightly worse than those of a conventional paraboloid. The larger the ratio of// A 
the better the radiation pattern. (The diameter D in the parabolic torus is the diamete 
of the illuminated area rather than the diameter of the torus itself.) The highest 
sidelobes produced by the parabolic torus do not lie within the principal planes. The 
inherent phase errors of the parabolic-torus surface due to its deviation from a true 



280 



Introduction to Radar Systems 



[Sec. 7.4 



parabola can cause sidelobes on the order of 15 db in intermediate planes. 25 These 
sidelobes usually lie in the 45° plane and are called eyes, because of their characteristic 
appearance on a contour plot of the radiation pattern. 

Theoretically, a torus with an elliptical cross section should result in less phase error 
and lower sidelobes than a torus with a parabolic cross section. 25 Experimental 
measurements, however, do not show a great difference in performance between the 
two; consequently, there is little basis for choosing between a torus with a parabolic or 
an elliptical cross section. 

A limited amount of beam scanning in the plane of the parabolic cross section can be 
had by moving the feed, just as in the conventional paraboloid. Wider scan angles in 

• Equal lengths of 
^wavequide 




Input 
horn 



Fig. 7.18. Principle of the organ-pipe scanner. 

this plane can be obtained by substituting a circular cross section for the parabolic 
cross section so that the resulting reflector is a portion of a sphere. Hence scanning is 
possible in both planes. This is the spherical reflector described above. 21 The sphere 
as an antenna is usually less effective (higher sidelobes, lower gain) than either the 
parabolic or the elliptical torus. 

In principle the parabolic torus can be scanned 180°, but because of beam spillover 
near the end of the scan and self-blocking by the opposite edge of the reflector, the 
maximum scan angle is usually limited to the vicinity of 120°. 

Only a portion of the parabolic-torus reflector is illuminated by the feed at any 
particular time. This may appear to result in low aperture utilization or poor efficiency 
since the total physical area is not related in a simple manner to the gain as it is in a fully 
illuminated antenna. However, the cost of the fixed reflector of the parabolic torus is 
relatively cheap compared with antennas which must be mechanically scanned. Non- 
utilization of the entire aperture is probably not too important a consideration when 
over-all cost and feasibility are taken into account. 



Sec. 7.4] 



Antennas 281 



The advantage of the parabolic torus is that it provides an economical method for 
rapidly scanning the beam of a physically large antenna aperture over a relatively wide 
scan angle with no deterioration of the pattern over this angle of scan. Its disadvantages 
are its relatively large physical size when compared with other means for scanning and 
the large sidelobes obtained in intermediate planes. 

Organ-pipe Scanner. Scanning the beam in the parabolic torus is accomplished by 
moving a single feed or by switching the transmitter between many fixed feeds. A 
single moving feed may be rotated about the center of the torus on an arm of length 
approximately one-half the radius of the torus. For example, a 120° torus antenna 




Fig. 7.19.. Thirty-six-horn organ-pipe scanner. {Courtesy U.S. Naval Research Laboratory.) 

might be scanned by continuously rotating three feeds spaced 120° apart on the spokes 
of a wheel so that one feed is always illuminating the reflector. Although this may be 
practical in small-size antennas, it becomes a difficult mechanical problem if the radius 
of the rotating arm is large. 

Scanning may also be accomplished by arranging a series of feeds on the locus of the 
focal points of the torus and switching the transmitter power from one feed to the next 
with an organ-pipe scanner. 27 " 29 The principle of the organ-pipe scanner is shown in 
Fig. 7.18. The transmission lines from the feeds are arranged to terminate on the 
periphery of a circle. A feed horn is rotated within this circle, transferring power from 
the transmitter to each feed or group of feeds in turn. The rotary horn may be flared to 
illuminate more than one elementary feed of the row of feeds. All the transmission 
lines in the organ-pipe scanner must be of equal length. 

The radiation pattern from a torus with a well-designed organ-pipe scanner changes 
but little until the beam reaches one end of the scanning aperture. At this point the 
energy appears at both ends of the aperture and two beams are found in the secondary 
pattern. The antenna cannot be used during this period of ambiguity, called the 
deadtime. In a model of the organ-pipe scanner shown in Fig. 7.19,36 elements were 



282 Introduction to Radar Systems r SEC 7 5 

f f:u th [f f a time - 2? The deadtime for ^is model is equivalent to rotation past two 
ot the 36 elements; consequently it was inoperative about 6 per cent of the time 

in Figs. 7.18 and 7.19 the feeds are shown on a straight line, but in the parabolic 
torus they would he on the arc of a circle. 

The many feed horns plus all the transmission lines of the organ-pipe scanner result 
in a relatively large structure with significant aperture blocking. Aperture blocking 
can be minimized by designing the parabolic portion of the torus as an offset parabola 
just as in the case of a paraboloid. p ' 

k 36 °°,I°o'".^- 30 " 32 , The P rinci P'e of the parabolic torus may be applied to scanning a 
beam 360 in one plane (Fig. 7.20). The antenna consists of a parabolic torus extending 



90% reflection for 
A component 




45° parallel wires 



Fig. 7.20. A 360° parabolic-torus antenna. (Courtesy Barab, Maraneoni, and Scott,™ IRE WESCON 
Conv. Record.) ° "^"t-own 

360° in azimuth and made up of parallel wire elements forming an angle of 45° with the 
vertical meridians. The polarization of the feed is also at 45°. This arrangement of 
the grid wires produces a barber-pole effect. The 45° tilt of the grid wires causes the 
wires on one side of the antenna to be perpendicular to those on the opposite side 
Radiation from the 45° feed is parallel to the grid wires which it faces, causing it to be 
reflected. Since the polarization of the reflected wave makes an angle of 90° with the 
grid wires on the opposite side of the structure, the surface appears transparent and the 
energy passes through relatively unimpeded. Only linear polarization is possible with 
this antenna. r 

7.5. Cassegrain Antenna 

The Cassegrain antenna is an adaptation to the microwave region of an optical 
technique invented in the seventeenth century by William Cassegrain, a contemporary 
ot Jsaac Newton. The Cassegrain principle is widely used in telescope design to obtain 
high magnification with a physically short telescope and allow a convenient rear 
location for the observer. Its application to microwave reflector antennas permits a 
reduction in the axial dimension of the antenna, just as in optics. It also permits 
greater flexibility in the design of the feed system and eliminates the need for lone 
transmission lines. 6 

The principle of the Cassegrain antenna is shown in Fig. 7.21a. The feed is located 
at the vertex of the parabolic reflector, and a subreflector is located in front of the 
parabola between the vertex and the focus. Parallel rays coming from a target (at 



Antennas 283 
Sec. 7.5] 

infinity) are reflected by the parabola as a convergent beam and are "«£«?£dbyfl£ 
hyperbolic subreflector, converging at the positio n of the feed. Th e ^ of the 
reflector images the feed so that it appears as a virtual image at the focal point ot toe 

^geometry of the Cassegrain reflector is shown in Fig. 7.21ft. The focus of the 
pa Iaboirat7andthefeedis 8 atr. The point** is ..hown at the ^Ws^nt 
k sometimes placed forward of the reflector nearer to the subreflector. 1 he points t 
LdTZtCconilte foci of the hyperbolic subreflector. Convergent spherical 
waves cteS at Xd incident on ^hyperbola will be ; reflect. a. a secon set of 
convergent spherical waves centered at F'. Any hyperbola with foci at F and * 



Parabolic /\ Parabola 

reflector ' x 





[a) 



ib) 



Fig 7 21. (a) Cassegrain antenna showing the hyperbolic subreflector and the feed at the vertex of 
the main parabolic reflector; (b) geometry of Cassegrain antenna. 

satisfies this property, and there exists a family of hyperbolic surfaces which could be 
used as the subreflector. The larger the subreflector, the nearer it will be to the main 
reflector and the shorter will be the axial dimension of the antenna assembly. However, 
a large subreflector results in large aperture blocking, which may be undesirable. A 
small subreflector reduces aperture blocking, but it has to be supported at a greater 
distance from the main reflector. Thus the choice of subreflector size must represent a 
compromise. The feed also contributes to aperture blocking since it removes a portion 
of the energy Figure 7.22 is an example of a simple Cassegrain antenna that was 
designed by Wheeler Laboratories for the Bell Telephone Laboratories. 

The principle of the Cassegrain antenna may be explained by considering the action 
of the subreflector as a hyperbolic mirror which images the feed to a point behind the 
subreflector at the focus of the parabola. The magnification of the hyperbolic mirror 
is (e + \M(e - 1) where e is the eccentricity. Magnification is also equal to the 
distance from the subreflector to the real focus divided by the distance from the sub- 
reflector to the virtual focus. The eccentricity of a hyperbola is always greater than 
unity and is defined as the ratio of the distance between the two conjugate foci divided 
by the constant difference between the two focal radii. (The focal radii of a point on 
the locus of the hyperbola are the straight lines which join the point to the foci. The 
difference between focal radii is a constant, no matter which point is chosen.) lhe 



284 Introduction to Radar Systems [Sec 7 5 

effective focal length of the Cassegrain is equal to the distance between Fand F' times 
liS^S^iSL: ^ M ^" ifi — ********** JfJfS 
One application of the Cassegrain antenna is as a monopulse-trackine-radar 
antenna^ Assume, for simplicity, a monopulse radar with a conventional fparabohc 
reflector fed by a two-feed-horn assembly tracking in a single plane. If the wo beams 




r^'S c .) EXamP ' e ° f 3 SimP ' e CaSSegraln antEnna - (C °""^ °f P - W - »~, Wheeler Labora- 

generated by each of the feeds are to overlap in space at their half-power points the 
spacing 5 between the effective phase centers of the two feeds must be ? 



i .(m ^ 



(7.20) 



where /= focal length 

D = diameter of antenna 
A = wavelength 

t^fn^u °u tWs ? rmU ' a k is assumed that the half-power beamwidth is given 
by 6SX/D, and the beam-deviation proportionality factor is taken to be 9 The fatter 
factor accounts for the deviation from Snell's law of reflection when the reflLtor a 

E butfofthe ° f a flat P, f e , (Ref ' '' P" 488 >- In ^y ^is is a functln of h } ^ 
ratio, but for the purpose of this example it is assumed to be constant. 



_ ,, Antennas 285 

Sec. 7.5] 

Eauation (7.20) gives a limitation on the minimum value of///) ratio. If the phase 
centers of the two feed horns were one wavelength apart, Eq. (7.20) indicates that the 
flD ratio would have to approximate unity. This is a large value off/D for a reflector- 
type antenna. In an antenna with f\D « 1 , the feed structure is relatively far out on 
the axis of the reflector and the mechanical problem of supporting the feeds becomes 
more difficult than if the///) ratio were small. The closest the feeds might be spaced is 
one-half wavelength (open-ended waveguides placed side by side) The///) ratio in 
this case is 5, which is still larger than most conventional parabolic reflectors but is 
within manageable proportions. Open-ended waveguides may be spaced closer than 
one-half wavelength if they are filled with dielectric. The dielectric reduces the 
minimum size of waveguide which can be used at a particular frequency. Dielectric- 
filled guide, however, is of higher loss than air-filled guide and usually has less power- 
handling capability. . _ 
The magnifying property of the Cassegrain antenna permits the use of a parabola ot 
conventional///) ratio to obtain the same effect as a parabola with a larger//!) For 
example, a Cassegrain antenna configuration using a paraboloid with///) = 35 and 
a hyperboloid with a magnification of 3 results in an effective///) of 1 .05. The feeds at 
the real focus F' of the Cassegrain antenna must be larger than those at the focus of a 
conventional parabola because of the magnifying action of the hyperbolic reflector. 
It has been claimed that the over-all length of a paraboloid antenna can be reduced by a 
factor of two when redesigned with the Cassegrain configuration. 33 

An important advantage of the Cassegrain configuration for monopulse-radar 
application is that the RF plumbing can be placed behind the reflector, avoiding the 
long runs of transmission line to the focus needed in a conventional paraboloid. The 
longer the transmission line, the greater is the chance that there will be differences in 
the phases between the lengths of the transmission lines and, hence, errors in the 
monopulse angle measurement. 

The elimination of long runs of transmission lines with the Cassegrain antenna is 
important when low-noise receivers such as masers or parametric amplifiers are used. 
The loss in the transmission line can significantly degrade the sensitivity of the receiver. 
In the Cassegrain antenna the low-noise receivers can be placed directly at the feed horn. 
To do the same with the conventional paraboloid antenna would require the receivers, 
or at least the front ends of the receivers, to be suspended out at the focus in front of the 
antenna. This not only increases the mechanical design problem, but it also results in 
increased aperture blocking. 

The Cassegrain antenna configuration can be used to generate a multitude ot over- 
lapping beams from a single reflector by placing in the vicinity of the vertex of the 
paraboloid a separate feed for each beam. The Cassegrain geometry permits scanning 
of a single beam by mechanically moving a single feed at the vertex or by switching 
among many feeds as with an organ-pipe scanner. It can also be scanned by moving 
one of the antenna surfaces. 34 - 36 

The presence of the subreflector in front of the main reflector in the Cassegrain 
configuration causes aperture blocking. Part of the energy is removed, resulting in a 
reduction of the main beam and an increase in the sidelobes. If the parabolic reflector 
is circular and assumed to have a completely tapered parabolic illumination, a small 
circular obstacle in the center of the aperture will reduce the (power) gain by approxi- 
mately [1 - 2(DJD) 2 ] 2 , where D h is the diameter of the obstacle (hyperbolic sub- 
reflector) and D is the diameter of the main aperture. 34 The relative (voltage) level of 
the first sidelobe is increased by (2DJD) 2 . For example, if the factor DJD were equal 
to 0.122, the gain would be lower by about 0.3 db and a -20-db sidelobe would be 
increased to about — 1 8 db. 

Aperture blocking may be reduced by decreasing the size of the subreflector. By 



286 Introduction to Radar Systems 



[Sec. 7.5 



Main reflector with 
polarization twister 
(twist reflector) 



making the feed more directive, or by moving it closer to the subreflector, the size of the 
subreflector may be reduced without incurring a spillover loss. However the feed 
cannot be made too large since it partially shadows the energy reflected from the main 
parabolic reflector. Minimum total aperture blocking occurs when the feed size and 

distance are such that the shadows produced by 
the subreflector and the feed are of equal area. 34 
If operation with a single polarization is 
permissible, the technique diagramed in Fig. 
7.23 can considerably reduce aperture blocking. 
The subreflector consists of a horizontal grating 
of wires, called a transreflector, which passes 
vertically polarized waves with negligible atten- 
uation but reflects the horizontally polarized 
( ^■""■poi. — - — _* wave radiated by the feed. The horizontally 

^"SJ Hor. poi. | polarized wave reflected by the subreflector is 

rotated by the twistreflector at the surface of the 
main dish. The twistreflector is equivalent to 
a quarter-wave plate which produces a 90° 
rotation of the plane of polarization (Ref. 1, 
Sec. 12. 10). The wave reflected from the main 
dish is vertically polarized and passes through 
the subreflector with negligible effect. The 
subreflector is transparent to vertically polar- 
ized waves and does not block the aperture. 
Some aperture blocking does occur, however, 
because of the feed, but this blocking can be 
made small and comparable with that of an 
ordinary parabolic-reflector design. 34 





Subreflector with 
polarization - 
dependent surface 



Fig. 7.23. Polarization-twisting Cassegrain 
antenna. Aperture blocking by the sub- 
reflector is reduced with this design. 



7.6. Lens Antennas 

The most common type of radar antenna is the parabolic reflector in one of its 
various forms. The microwave paraboloid reflector is analogous to an automobile 
headlight or to a searchlight mirror. The analogy of an optical lens is also found in 
radar (an example is the radar of Fig. 1.8). Lens and reflector antennas are often 
interchangeable in microwave systems since they both convert a spherical wave to a 
plane wave, or vice versa. Three types of microwave lenses applicable to radar are 
(I) dielectric lenses, (2) metal-plate lenses, and (3) lenses with nonuniform index of 
refraction. 

Dielectric Lenses. 2 The homogeneous, solid, dielectric-lens antenna of Fig 7 24a is 
similar to the conventional optical lens. A point at the focus of the lens produces a 
plane wave on the opposite side of the lens. Focusing action is a result of the difference 
in the velocity of propagation inside the dielectric as compared with the velocity of 
propagation in air. The index of refraction n of a dielectric is defined as the speed of 
light in free space to the speed of light in the dielectric medium. It is equal to the 
square root of the dielectric constant. Materials such as polyethylene, polystyrene 
Plexiglas, and Teflon are suitable for small microwave lenses. They have low loss and 
may be easily shaped to the desired contour. Since the velocity of propagation is 
greater in air than in the dielectric medium, a converging lens is thicker in the middle 
than at the outer edges, just as in the optical case. Dielectric lenses may be designed 
using the principles of classical geometric optics. 

One of the limitations of the solid homogeneous dielectric lens is its thick size and 
large weight. Both the thickness and the weight may be reduced considerably bv 
stepping or zoning the lens (Fig. 7.24*). Zoning is based on the fact that a 360° change 



Sec. 7.6] Antennas 287 

of phase at the aperture has no effect on the aperture phase distribution . Starting with 
zero thickness at the edge of the lens, the thickness of the dielectric is progressively 
increased toward the lens axis as in the design of a normal lens. However, when the 
path length introduced by the dielectric is equal to a wavelength, the path in the dielectric 
can be reduced to zero without altering the phase across the aperture. The thickness 
of the lens is again increased in the direction of the axis according to the lens design 
until the path length in the dielectric is once more 360°, at which time another step may 
be made. The optical path length through each of the zones is one wavelength less 



Focus v/////a Focus 





(*> 

Fig. 7.24. (a) Converging-lens antenna constructed of homogeneous solid dielectric. Direct micro- 
wave analogy of optical lens, (b) Zoned dielectric lens. 

than the next outer zone. If the thickness of the path length removed from the lens is 
t, the net change in the optical path length is /ut — t, where fx is the index of refraction. 
This change in path length must be equal to one wavelength or to some integral multiple 
of a wavelength. 

Although zoning reduces the size and weight of a lens, it is not without disadvantages. 
Dielectric lenses are normally wideband; however, zoning results in a frequency- 
sensitive device. Another limitation is the loss in energy and increase in sidelobe level 
caused by the shadowing produced by the steps. The effect of the steps may be 
minimized by using a design with large// D, on the order of 1 or more. Even with these 
limitations, a stepped lens is usually to be preferred because of the significant reduction 
in weight. 

The larger the dielectric constant (or index of refraction) of a solid dielectric lens, the 
thinner it will be. However, the larger the dielectric constant, the greater will be the 
mismatch between the lens and free space and the greater the loss in energy due to 
reflections at the surface of the lens. Compromise values of the index of refraction lie 
between 1 .5 and 1.6. Lens reflections may also be reduced with transition surfaces as 
in optics. These surfaces should be a quarter wave thick and have a dielectric constant 
which is the square root of the dielectric constant of the lens material. 

Artificial Dielectrics.™-* 2 Instead of using ordinary dielectric materials for lens 
antennas, it is possible to construct them of artificial dielectrics. The ordinary di- 
electric consists of molecular particles of microscopic size, but the artificial dielectric 
consists of discrete metallic or dielectric particles of macroscopic size. The particles 
may be spheres, disks, strips, or rods imbedded in a material of low dielectric constant 
such as polystyrene foam. The particles are arranged in some particular configuration 
in a three-dimensional lattice. The dimension of the particles in the direction parallel 
to the electric field as well as the spacing between particles should be small compared 
with a wavelength. If these conditions are met, the lens will be insensitive to fre- 
quency. 



288 Introduction to Radar Systems [Sec. 7.6 

When the particles are metallic spheres of radius a and spacing s between centers the 
dielectric constant of the artificial dielectric is approximately 

477a 3 

(7.21) 



*=!+' 



assuming no interaction between the spheres. 41 

An artificial dielectric may also be constructed by using a solid dielectric material 
with a controlled pattern of voids. This is a form of Babinet inverse of the more usual 



£ 
©- 



E 

L » 



£ 

,1 




Direction of 
propagation 



Fig. 7.25. Plan, elevation, and end views of a converging lens antenna constructed from parallel-plate 
waveguide. (£-plane metal-plate lens.) v 

artificial dielectric composed of particles imbedded in a low-dielectric-constant ma- 
terial. 43 The voids may be either spheres or cylinders, but the latter are easier to 
machine. 

Lenses made from artificial dielectrics are generally of less weight than those from 
solid dielectrics. For this reason, artificial dielectrics are often preferred when the 
size of the antenna is large, as, for example, at the lower radar frequencies. Artificial- 
dielectric lenses may be designed in the same manner as other dielectric lenses. 

Metal-plate Lens.**- 1 " An artificial dielectric may be constructed with parallel- 
plate waveguides as shown in Fig. 7.25. The phase velocity in parallel-plate waveguide 
is greater than that in free space ; hence the index of refraction is less than unity. This 
is opposite to the usual optical refracting medium. A converging metal-plate lens is 
therefore thinner at the center than at the edges, as opposed to a converging dielectric 
lens which is thinner at the edges. The metal-plate lens shown in Fig. 7.25 is an 
£-plane lens since the electric-field vector is parallel to the plates. Snell's law is obeyed 
in an £-plane lens, and the direction of the rays through the lens is governed by the 
usual optical laws involving the index of refraction. 

The surface contour of a metal-plate lens is, in general, not parabolic as in the case of 
the reflector. 5 For example, the surface closest to the feed is an ellipsoid of revolution 
if the surface at the opposite face of the lens is plane. 

The spacing s between the plates of the metal-plate lens must lie between A/2 and X if 
only the dominant mode is to be propagated. The index of refraction for this type of 
metal-plate lens is 



V 



1 



-<3\ 



(7.22) 



Sec. 7.6] Antennas 289 

where A is the wavelength in air. Equation (7.22) is always less than unity. At the 
upper limit of spacing, s = X, the index of refraction is equal to 0.866. The closer the 
spacing, the less will be the index of refraction and the thinner will be the lens. How- 
ever, the spacing, and therefore the index of refraction, cannot be made arbitrarily 
small since the reflection from the interface between the lens and air will increase just 
as in the case of the solid-dielectric lenses. For a value of s = A/2, the index of re- 
fraction is zero and the waveguide is beyond cutoff. The wave incident on the lens will 
be completely reflected. In practice, a compromise value of /a between 0.5 and 0.6 is 
often selected, corresponding to plate spacings of 0.557A and 0.625A and to power 
reflections at normal incidence of 1 1 and 6.25 per cent, respectively (Ref. 1, p. 410). 



-*-£" 




Fig. 7.26. Zoned metal-plate lens. 

Even with an index of refraction in the vicinity of 0.5 to 0.6, the thickness of the metal- 
plate lens becomes large unless inconveniently long focal lengths are used. The 
thickness may be reduced by zoning (Fig. 7.26) just as with a dielectric lens. The 
bandwidth of a zoned metal-plate lens is larger than that of an unzoned lens, but 
the steps in the lens contour scatter the incident energy in undesired directions, reduce 
the gain, and increase the sidelobe level. 

Another class of metal-plate lens is the constrained lens, or path-length lens, in which 
the rays are guided or constrained by the metal plates. In the //-plane metal-plate 
constrained lens, the electric field is perpendicular to the plates (H field parallel); thus 
the velocity of the wave which propagates through the plates is relatively unaffected 
provided the plate spacing is greater than 1\2. The direction of the rays is'not affected 
by the refractive index, and Snell's law does not apply. Focusing action is obtained by 
constraining the waves to pass between the plates in such a manner that the path length 
can be increased above that in free space. 

An example of a particular constrained lens with plates slanted at an angle d is shown 
in Fig. 7.27. The index of refraction is simply n = sec 6, where d is the angle between 
the direction of the plates and the lens axis. When this lens has a flat front surface as 
shown in the figure, the curved side toward the feed is a hyperboloid of revolution. A 
disadvantage of this constrained lens is that the £-plane radiation pattern has a low 
gain and is very distorted, with high sidelobes on one side of the axis. The constrained 
lens of Fig. 7.27 is usually unsuited for radar applications. 37 Other techniques for 
obtaining //-plane metal-plate constrained lenses are described in the literature. 37 - 41 

Still another type of constrained lens is shown in Fig. 7.28. 47 The rays are guided or 
constrained by the metal plates, and Snell's law is not obeyed. This lens differs from 
the constrained lens described above since it is cylindrical, and the E field is parallel 
rather than perpendicular to the plates. The latter characteristic might cause this lens 
to be classified with the £-plane lens of Fig. 7.25, but the lens of Fig. 7.28 focuses by 
constraining the wave while the other .E-plane lens employs Snell's law to achieve 
focusing action. The construction of the £-plane constrained lens is simple since it 
consists only of rectangular plates. Focusing is obtained normal to the constrained 
plates (normal to the electric vector). A 72- wavelength lens at a wavelength of 1 .25 cm 
with an///) = 1.5 produced a 1° beam which could be scanned over a 100° sector by 
positioning the feed. 47 



290 Introduction to Radar Systems 



[Sec. 7.6 



Focus 




Fig. 7.27. Example of a constrained metal-plate lens constructed of slanted plates. Index of re- 
fraction = sec 8. Dashed lines represent ray paths. (After Kock, 46 Proc. IRE.) 

Lens Tolerances. In general, the mechanical tolerances for a lens antenna are less 
severe than for a reflector. A given error in the contour of a mechanical reflector 
contributes twice to the error in the wavefront because of the two-way path on reflection. 
Mechanical errors in the lens contour contribute but once to the phase-front error. 
Fry and Goward 5 state that "the easy mechanical tolerances involved in the metal 
plate lens ... are the main advantage of a lens over a reflector." Although there may 




(a) 



E 
--©-- 



Focus < 



(b) 



Fig. 7.28. (a) Cylindrical constrained lens with £ field parallel to metal plates; (b) top view of lens. 
(After Ruze," Proc. IRE.) 



Sec. 7.6] Antennas 291 

be room for discussion concerning the advantages of a lens over a reflector and what 
the "main" advantage might be, the question of tolerances is nevertheless an important 
consideration. 

The derivation of the mechanical tolerances necessary to achieve a plane wavetront 
accurate to a specified value may be found in standard texts on antennas. 1 ' The 
maximum permissible error in the phase front depends upon the degree of importance 
attached to a loss of gain and to a deterioration of the antenna pattern. In many 
applications a phase variation across the wavefront of ±A/16(a maximum of A/8) is 
acceptable engineering practice. (The relationship between tolerances and antenna 
patterns is described in Sec. 7.11.) 

The tolerances required for lens antennas are given below for several lens types. 
The total phase variation across the aperture is taken to be A/8, or ±2/16 (p is the index 
of refraction). 

Tolerance on lens thickness t: 

•\ 

Dielectric lens dt = ± — p > 1 ( 7 - 23 ) 

160 - 1) 

Metal-plate lens dt = ± — P < 1 <- 7 - 24 ) 

16(1 - p) 

Tolerance on the index of refraction for a fully zoned lens: 

Dielectric lens dp = ±—(p-l) p > 1 ( 7 - 25 ) 

16 

3 

Metal-plate lens dp = ± — (I - p) P < 1 ( 7 - 26 ) 

16 

Since in a zoned lens (p — 1)/ «a A, we get dp = ±A 2 /16r. 
Tolerance on plate spacing s in a zoned metal-plate lens : 

6s =± ^ (7.27) 

16(1 + p) 

By comparison, the mechanical tolerance of a reflector antenna must be ±A/32 if the 
phase-front error is to be ±A/16, because of the two-way path due to reflection. 

A source of error in lenses not found in reflector antennas is the variation in the 
properties of the material. Both real and artificial dielectrics are not perfectly uniform 
from sample to sample or even within the same sample. 

Luneburg Lens. Workers in the field of optics have from time to time devised lenses 
in which the index of refraction varied in some prescribed manner within the lens. 
Although such lenses had interesting properties, they were only of academic interest 
since optical materials with the required variation of index of refraction were not 
practical. However, at microwave frequencies it is possible to control the index of 
refraction of materials (p is the square root of the dielectric constant e), and lenses with 
a nonuniform index of refraction are practical. 

One of the most important of the variable-index-of-refraction lenses in the field of 
radar is that due to Luneburg. 48 The Luneburg lens is spherically symmetric and has 
the property that a plane wave incident on the sphere is focused to a point on the surface 
at the diametrically opposite side. Likewise, a transmitting point source on the surface 
of the sphere is converted to a plane wave on passing through the lens (Fig. 7.29). 
Because of the spherical symmetry of the lens, the focusing property does not depend 
upon the direction of the incident wave. A Luneburg lens might be used where a 
rapidly scanned antenna over a wide angle is required. It might also have application 
where the antenna is mounted on an unstable base such as a ship. Stabilization of the 



292 Introduction to Radar Systems [Sec. 7.6 

beam may be obtained by adjusting the feed to compensate for the ship's motion. The 
beam may be scanned by positioning a single feed anywhere on the surface of the lens or 
by locating many feeds along the surface of the sphere and switching the radar trans- 
mitter or receiver from one horn to another as 
with an organ-pipe scanner. The Luneburg lens 
can also generate a number of fixed beams and is 
competitive in many applications with array- 
antenna beam forming. 

The index of refraction (x or the dielectric 
constant e varies with the radial distance in a 
Luneburg lens of radius r , according to the 
relationship 

j" = e* = 2- - (7.28) 




Fig. 7.29. Luneburg-lens geometry 
showing rays from a point source radi- 
ated as a plane wave after passage 
through the lens. 



The index of refraction is a maximum at the 
center, where it equals Vl, and decreases to a 
value of 1 on the periphery. 

The development of materials which exhibit a 
continuous variation of dielectric constant such 
as needed for the Luneburg-lens antenna was one 
of the limitations which had to be overcome by early experimenters. Practical three- 
dimensional Luneburg lenses have been constructed of a large number of spherical 
shells, each of constant index of refraction. Discrete changes in index of refraction 
approximate a continuous variation. In one example of a Luneburg lens (Fig. 7.30) 
10 concentric spherical shells are arranged one within the other. 49 - 50 The dielectric 
constant of the individual shells varies from 1.1 to 2.0 in increments of 0.1. The 
diameter of this stepped-index lens is 18 in., and the frequency of operation is X band. 
As many as 50 steps might be used in this type of design. 




Fig. 7.30. Hemispherical-half-shell construction of stepped-index Luneburg lens. {Courtesy Emerson 
and Cuming, Inc.) 




Sec. 7.6] Antennas 293 

The dielectric materials must not be too heavy, yet they must be strong enough to 
support their own weight without collapsing. They should have low dielectric loss and 
not be affected by the weather or by changes in temperature. They should be easily 
manufactured with uniform properties and must be homogeneous and isotropic if the 
performance characteristics are to be independent of position. 

The 1 8-in. Jf-band lens mentioned above was constructed from a polystyrene material 
called expandable beads. 49 These are discrete spheroids of polystyrene, the size of 
which is controlled during manufacture. By mixing the partially expanded beads with 
a higher-dielectric-constant material in proper 
proportions, a dry mixture capable of being 
molded is obtained. A baglike radome cover- 
ing the lens provides weather protection. 
Another promising technique for the con- 
struction of large Luneburg lenses, especially 
at UHF, is the use of artificial dielectrics. 51 

The antenna pattern of a Luneburg lens has 
a slightly narrower beamwidth than that of a 
paraboloidal reflector of the same circular \ \ 

cross section, but the sidelobe level is \ \ j A 

greater. 52 " 56 This is due to the fact that the S^'A"'' ^S 

paths followed by the rays in a Luneburg lens jm„gi! f 5 ; ~\- " " radiation 

tend to concentrate energy toward the edge of P° int source/ JX« tinq 

the aperture. Thus the aperture distribution surface 

of the Luneburg lens is not as tapered as that fig. 7.31. Hemispherical Luneburg lens 
of a paraboloid, assuming the same type of with plane reflecting surface on the base, 
feed illuminates both antennas. The natural 

tendency for illuminated energy to concentrate at the edges of the lens makes it difficult 
to achieve extremely low sidelobes. In practice, the sidelobe level of a Luneburg lens 
seems to be in the vicinity of 20 to 22 db. 56 

When the full 4tt radians of solid coverage is not required, a smaller portion of the 
lens can be used, with a saving in size and weight. 51 - 57 If only hemispherical coverage 
is needed (2tt solid radians) the lens shown in Fig. 7.3 1 can be used. A plane reflecting 
surface is placed at the base of the hemisphere to image the feed at S into a virtual source 
at S'. Movement of the source 5 causes a corresponding movement of the beam in the 
opposite direction. There is some deterioration of the feed pattern in the hemispherical 
lens shown in Fig. 7.31 since a portion of the energy emitted by the source misses the 
reflector entirely and is lost. The sidelobes resulting from the missed radiation may be 
reduced with absorbent material to absorb the nonreflected energy, 51 or the reflecting 
plane can be extended beyond the base of the hemisphere to reflect these rays in the 
proper direction. A possible disadvantage of a hemispherical lens when compared 
with the full spherical lens is that the feed causes aperture blocking. 

If the scanning sector is less than 277 radians, a smaller lens can be had by constructing 
only a spherical wedge of the Luneburg lens; that is, the lens is included between two 
plane reflectors which pass through the lens center. 

The Luneburg-lens principle can also be applied as a passive reflector in a manner 
analogous to a corner reflector. 51 If a reflecting cap is placed over a portion of the 
spherical lens, an incident wave emerges in the same direction from which it entered. 
The cap may be made to cover a sector as large as a hemisphere. The Luneburg 
reflector is effective over a much greater solid angle than the corner reflector. 

The Luneburg principle may also be applied to a two-dimensional lens which scans a 
fan beam in one plane. Since the two-dimensional version is simpler than a three- 
dimensional one, it was the first type to be constructed. A geodesic analog of a 




294 Introduction to Radar Systems [Sec. 7.7 

two-dimensional Luneburg has been applied in a ^-band mortar-location radar. 58 In 
the geodesic analog the variation in dielectric constant is obtained by the increased 
path length for the RF energy traveling in the TEM mode between parallel plates. 51 - 59 
The result is a dome-shaped parallel-plate region as shown in Fig. 7.32. In the mortar 
radar application a fan beam generated by the two-dimensional Luneburg was converted 
to a pencil beam by a cylindrical reflector. The lens acted as the feed for the reflector. 
Two^ vertical beams were generated in this radar. Each beam had a width of 0.76 and 
1.06° in the vertical and horizontal planes, respectively, and was separated in the 

vertical by an angle of 1.85°. The antenna 
scanned a 40° azimuth sector at a rate of 17 
scans per beam per second. 

Other types of lenses based on the principle 
of nonuniform index of refraction have been 
described by Kelleher, 56 Huynen, 60 and 
others. 184 

Fig. 7.32. The "tin-hat" geodesic analog of Evaluation of Lenses as Antennas. One of 
a two-dimensional Luneburg lens. the major advantages of a lens over a reflector 

antenna is the absence of aperture blocking. 
Considerable equipment can be placed at the focus of the lens without interfering with 
the resultant antenna pattern. Reflections from the lens surface which cause a signifi- 
cant mismatch at the feed can also be eliminated or reduced without significantly 
degrading the pattern by tilting the feed slightly off axis to avoid the back reflection. 
Another advantage of the lens is that mechanical and electrical tolerances are more 
relaxed than in the reflector antenna. 

The lens is capable of scanning the radiated beam over a wide angle by positioning 
the feed. Theoretically, the Luneburg lens can scan the complete sphere (4n solid 
radians). Constrained metal-plate lenses are capable of very wide scan angles as 
compared with the limited scanning possible by moving the feed in a paraboloid 
reflector. Solid dielectric lenses can also achieve reasonably wide scan angles by 
properly designing the contour of both surfaces of the lens. 61 A homogeneous di- 
electric sphere may be scanned through 4tt solid radians if the index of refraction is not 
too high and if the diameter is not greater than about 30A. 62 

One of the disadvantages of the lens is that it is usually less efficient than comparable 
reflector antennas because of dielectric losses in the materials, reflections from the lens 
surfaces, or scattering from the steps in a zoned lens. Although it is dangerous to 
generalize, additional losses from these sources in a stepped lens might be 1 or 2 db. 40 
The lack of suitable solid or artificial dielectric materials has limited the development 
of lenses. The problem of dissipating heat from large dielectric lenses, such as the 
Luneburg, can sometimes restrict their use to moderate-power or receiving appli- 
cations. Conventional lenses are usually large and heavy, unless zoned. To reduce 
the loss caused by scattering from the steps in a zoned lens, the ratio of the focal length 
/to the antenna diameter D must be made large. The//Z> ratio of zoned lenses might 
be of the order of unity or more. Lenses which must scan by positioning of the feed 
should also have large fjD ratio. A large///) requires a greater mechanical structure 
because the feeds are bigger and must be supported farther from the lens. 

7.7. Array Antennas 

An array antenna consists of a number of individual radiating elements suitably 
spaced with respect to one another. The relative amplitude and phase of the signals 
applied to each of the elements are controlled to obtain the desired radiation pattern 
from the combined action of all the elements. The radiating elements might be dipoles, 
waveguide horns, or any other type of antenna. An array consists of no less than two 



s 7 7 -i Antennas 295 

elements The maximum number is limited only by practical considerations. There 
is no fundamental reason why array antennas containing large numbers of elements 
(thousands, ten of thousands, or more) could not be built if it were necessary to do so. 

The array antenna differs in concept from both the lens and the reflector. The lens 
and the reflector apply the proper phase relationships to the wavefront after it is 
radiated by the point-source feed. The shape of the wavefront on leaving the feed is 
spherical It is converted to a plane wave by the action of the lens or the reflector. In 
the array antenna, the proper phase relationships are applied to the signal before it is 
radiated, that is, in the transmission lines feeding the individual elements. 

Just as with any other radiating aperture, the distribution needed across the array to 
achieve the desired far-field radiation pattern may be determined from Fourier-trans- 
form theory The uniform amplitude distribution results in maximum efficiency but 
large sidelobes A tapered distribution results in lower sidelobes at the expense ol 
reduced efficiency. Unlike other radar antennas, the phase distribution across the 
aperture of an array can be readily controlled and is one of the characteristics which 
distinguish the design of a radar system using an array from one which uses a lens or a 

reflector. . . . , 

The relative phases between the elements determine the position of the main beam. 
If the phases are fixed, the antenna radiation pattern is also fixed. Scanning of the 
beam formed by an array can be accomplished by mechanically moving the entire 
array-antenna structure. However, the beam can also be steered by varying the rela- 
tive phase shift between the elements of the array. 

Two common geometrical forms of array antennas of interest in radar are the linear 
array and the planar array. A linear array consists of elements arranged in a straight 
line in one dimension. A planar array is a two-dimensional configuration of elements 
arranged to lie in a plane. The planar array may be thought of as a linear array of linear 
arrays A broadside array is a linear or a planar array in which the direction of maxi- 
mum radiation is perpendicular, or almost perpendicular, to the line (or plane) of the 
array An endfire array has its maximum radiation parallel to the array. 

The linear array generates a fan beam when the phase relationships are such that the 
radiation is perpendicular to the array. When the radiation is at some angle other 
than broadside, the radiation pattern is a conical-shaped beam. The broadside linear- 
array antenna may be used where broad coverage in one plane and narrow beamwidth 
in the orthogonal plane are desired. The linear array can also act as a feed for a para- 
bolic-cylinder antenna. The combination of the linear-array feed and the parabolic 
cylinder generates a more controlled fan beam than is possible with either a simple 
linear array or with a section of a parabola. The combination of a linear array and 
parabolic cylinder can also generate a pencil beam. 

The endfire array is a special case of the linear or the planar array when the beam is 
directed along the array. Endfire linear arrays have not been widely used in radar 
applications. They are usually limited to low or medium gains since an endfire linear 
antenna of high gain requires an excessively long array. Small endfire arrays are 
sometimes used as the radiating elements of a broadside array if directive elements are 
required. Linear arrays of endfire elements are also employed as low-silhouette 

antennas. „ . ^ . . , „ 

The two-dimensional planar array is probably the one of most interest in radar 
applications since it is fundamentally the most versatile of all radar antennas. A 
rectangular aperture can produce a fan-shaped beam. A square or a circular aperture 
produces a pencil beam. The array can be made to simultaneously generate many 
search and/or tracking beams with the same aperture. 

Many of the early radars developed in the late 1930s used array antennas The 
frequencies of these radars were relatively low (VHF or lower UHF) compared with 



296 Introduction to Radar Systems [Sec. 7.7 

later radars, although they were high for that period. Large-aperture antennas can be 
designed at VHF and UHF with relatively few radiating elements. The array antenna 
was also used extensively in communications work prior to World War II and its 
performance and design were probably better understood by the preradar 'antenna 
engineer than were reflector antennas or lenses. Because large antenna apertures are 
necessary for high-performance, long-range radars, the array is more practical at lower 
frequencies than at higher frequencies, since more elements are required to fill the same 
physical aperture at the higher frequencies. 

Other types of array antennas are possible than the linear or the planar arrangements 
For example, the elements might be arranged on the surface of a cylinder to obtain 360° 
coverage (360 coverage may also be obtained with a number of planar arrays) The 
radiating elements might also be mounted on the surface of a sphere, or indeed on an 
object of any shape, provided the phase at each element is that needed to give a plane 
wave when the radiation from all the elements is summed in space. 

Interest in array antennas for radar applications waned with the development of 
microwave radar and the application of optical techniques to microwaves The 
reflector proved to be a simpler antenna than the array in the sizes required for micro- 
wave frequencies. It was more convenient to design and manufacture and was reliable 
in operation The reflector is a popular form of antenna and one difficult to displace 
by rnore sophisticated techniques. 

In the 1950s, as interest in extremely long range radars increased, the array antenna 
received renewed attention, primarily because of its inherent ability to electronically 
steer a beam without the necessity of moving large mechanical structures. This is an 
important advantage if the antenna is large. Other advantages of the array are that 
more than one beam can be generated with the same aperture, large peak powers can be 
radiated, and the aperture illumination can be more readily controlled than in a single- 
feed antenna. Lower sidelobes can be achieved, in principle. It is the flexibility 
ottered by the many individually controlled elements in an array antenna that makes it 
attractive for radar applications. However, the ability to control each individual 
element results in a complex and expensive radar. Its major disadvantages when 
compared with more conventional antennas are its high cost and the complexity 
resulting from the many additional components. 

An array in which the relative phase shift between elements is controlled by electronic 
devices is called an electronically scanned array. In an electronically scanned array the 
antenna elements, the transmitters, the receivers, and the data-processing portions of 
the radar are often designed as a unit. A given radar might work equally well with a 
mechanically positioned array, a lens, or a reflector antenna if they each had the same 
radiation pattern, but such a radar could not be converted efficiently to an electronically 
scanned array by simple replacement of the antenna alone because of the interdepend- 
ence of the antenna and the other portions of the radar. 

Radiation Pattern?,™- 1 * Consider a linear array made up of N elements equally 
spaced a distance d apart (Fig. 7.33). The elements are assumed to be isotropic point 
sources radiating uniformly in all directions with equal amplitude and phase. Although 
isotropic elements are not realizable in practice, they are a useful concept in array 
theory, especially for the computation of radiation patterns. The effect of practical 
elements with nonisotropic patterns will be considered later. The array is shown as a 
receiving antenna for convenience, but because of the reciprocity principle, the results 
obtained apply equally well to a transmitting antenna. The outputs of all the elements 
are summed via lines of equal length to give a sum output voltage E a . Element 1 will 
be taken as the reference signal with zero phase. The difference in the phase of the 
signals in adjacent elements is y> = 2M.d/X) sin 6, where 6 is the direction of the incoming 
radiation . It is further assumed that the amplitudes and phases of the signals at each 



Antennas 



297 



Sec. 7.7] 

element are weighted uniformly. Therefore the amplitudes of the voltages in each 
element are the same and, for convenience, will be taken to be unity. The sum of all 
the voltages from the individual elements, when the phase difference between adjacent 
elements is y, can be written 

E a = sin cot + sin (cot + y) + sin (cot + 2y) + h sin [cot + (N - l)y] (7.29) 

where co is the angular frequency of the signal. The sum can be written 66 



sin 



cot + (N - 1) 



y 



sin (JVy/2) 



sin (y/2) 



(7.30) 



The first factor is a sine wave of frequency to with a phase shift (N — l)y/2 (if the phase 
reference were taken at the center of the array, the phase shift would be zero), while the 



Incoming signal 




Fig. 7.33. TV-element linear array. 

second term represents an amplitude factor of the form sin (iVy/2)/sin (y/2). The 
radiation pattern is equal to the normalized square of the amplitude, or 



G a (6) 



\Ef sin 2 [NirjdlX) sin 0] 
N 2 ~ N 2 sin 2 \jr(djX) sin 0] 



(7.31) 



If the spacing between antenna elements is A/2 and if the sine in the denominator of 
Eq. (7.3 1) is replaced by its argument, the half-power beamwidth is approximately equal 
to 

= 10L8 (7 32) 

N 

The first sidelobe, for N sufficiently large, is 13.5 db below the main beam, and the 
height of the last sidelobe is 1 jN 2 (Ref. 1 , p. 268). The pattern of a uniformly illumi- 
nated array with elements spaced A/2 apart is similar to the pattern produced by a 
continuously illuminated uniform aperture [Eq. (7.16)]. 

Equation 7.31 predicts a second beam equal in magnitude to the main beam, but 
displaced by 180°. To avoid ambiguities and confusion, this backward radiation is 
usually eliminated by placing a reflecting or an absorbing screen behind the antenna 
array. For this reason only the radiation over the forward half of the antenna 
(—90° < 6 < 90°) is considered. 

As long as the spacing between elements of the array is K\2 or less, the sidelobe 
radiation will be small compared with the main beam. When the spacing between 



298 Introduction to Radar Systems [Sec. 7.7 

elements is greater than half a wavelength, additional lobes can appear in the antenna 
radiation pattern with amplitude equal to that of the main beam. These are called 
grating lobes, or secondary principal maxima. They are due to the radiation from the 
elements adding in phase in those directions for which the relative path lengths are 
integral multiples of 2tt radians. The positions of the grating lobes can be found from 
Eq. (7.31). They occur whenever both the numerator and the denominator are zero, 
or when tt(<//A) sin 6 = 0, n, 2v, etc. For example, when the spacing d between 
elements is two wavelengths, grating lobes will occur at 6 = ±30° and 6 = ±90°. 

If the grating lobes are allowed to exist, they might lead to confusion, since targets 
viewed by the grating lobes cannot be distinguished from targets viewed by the main 
beam. Therefore the element spacing should be no greater than a half wavelength if 
full ±90° coverage is desired. If less than full coverage is satisfactory, the grating lobes 
produced in a widely separated array can be reduced or eliminated over a smaller 
scanning range by elements with directive rather than isotropic radiation patterns. 
When directive elements are used, the resultant array antenna radiation pattern is 

G(6) = GM N^H^l = <***&) (7-33) 

N sin"* lTT(d/A) sin v\ 

where G e (Q) is the radiation pattern of an individual element. The resultant radiation 
pattern is the product of the element factor G e {6) and the array factor G a (0), the latter 
being the pattern of an array composed of isotropic elements. The array factor has 
also been called the space factor. Grating lobes caused by a widely spaced array may 
therefore be eliminated with directive elements which radiate little or no energy in the 
directions of the undesired lobes. 

Equation (7.33) is only an approximation, which may be seriously inadequate for 
many problems of array design. It should be used with caution. It ignores mutual 
coupling, 67 and it does not take account of the scattering or diffraction of radiation by 
the adjacent array elements or of the outward-traveling-wave coupling. 68 These 
effects cause the element radiation pattern to be different when located within the 
array in the presence of the other elements than when isolated in free space. 

In order to obtain an exact computation of the array radiation pattern, the pattern of 
each element must be measured in the presence of all the others. The array pattern 
may be found by summing the contributions of each element, taking into account the 
proper amplitude and phase. 

In a two-dimensional, rectangular planar array, the radiation pattern may some- 
times be written as the product of the radiation patterns in the two planes which con- 
tain the principal axes of the antenna, If the radiation patterns in the two principal 
planes are G^dJ and G 2 (d a ), the two-dimensional antenna pattern is 

G(6M = GtfJGJBJ (7.34) 

Note that the angles 6 e and 6 a are not necessarily the elevation and azimuth angles 
normally associated with radar. 70 . 183 The normalized radiation pattern of a uniformly 
illuminated rectangular array is 

G(0 d ) = si " 2 l>K<*M) sin fl„l sin 2 iMnjd/X) sin flj 

" ° N 2 sin 2 |>(d/A) sin 0J M 2 sin 2 [^d/A) sin B J ( } 

where TV = number of radiating elements in d a dimension with spacing d 
M = number in d e dimension 
Beam Steering. The beam of an array antenna may be steered rapidly in space 
without moving large mechanical masses by properly varying the phase of the signals 
applied to each element. Consider an array of equally spaced elements. The 
spacing between adjacent elements is d, and the signals at each element are assumed 



Sec. 7.7] Antennas 299 

of equal amplitude. If the same phase is applied to all elements, the relative phase 
difference between adjacent elements is zero and the position of the main beam will be 
broadside to the array at an angle = 0. The main beam will point in a direction 
other than broadside if the relative phase difference between elements is other than 
zero The direction of the main beam is at an angle O when the phase difference .is 
</> = 2t7(J/A) sin O . The phase at each element is therefore </> c + m0, where m - 
0, 1, 2, . . . , (N - 1), and </> c is any con- 



V 





Zm 




stant phase applied to all elements. The 
normalized radiation pattern of the ar- 
ray when the relative phase difference be- 
tween adjacent elements is <f> is given by | 

sin 2 [JV77(rf/A)(sin - sin fl )] L . ' 

() N 2 sin 2 |XdM)(sin - sin O )] I 

(7.36) p IG . 7.34. Steering of an antenna beam with 
The maximum of the radiation pattern variable-phase shifters (parallel-fed array). 

occurs when sin = sin O . 

Equation (7.36) states that the main lobe of the antenna pattern may be positioned to 
an angle O by the insertion of the proper phase shift <£ at each element of the array. 
If variable, rather than fixed, phase shifters are used, the beam may be steered as the 
phase is changed (Fig. 7.34). The phase-shifting device might be either mechanically 
or electronically controlled . Steering of the beam with mechanical or electronic phase 
shifters results in scanning speeds orders of magnitude greater than can be obtained by 
mechanically positioning the entire antenna structure. 

Change ofBeamwidth with Steering Angle. The half-power beamwidth in the plane 
of scan increases as the beam is scanned off the broadside direction. The beamwidth is 
approximately inversely proportional to cos O , where O is the angle measured from the 
normal to the antenna. This may be proved by assuming that the sine in the denomi- 
nator of Eq. (7.36) can be replaced by its argument, so that the radiation pattern is 
of the form (sin 2 u)/u 2 , where u = Nw(d/ X)(sin - sin O ). The (sin 2 u)/u 2 antenna 
pattern is reduced to half its maximum value when u = ±0.443tt. Denote by + the 
angle corresponding to the half-power point when > O , and 0_, the angle correspond- 
ing to the half-power point when < O ; that is, + corresponds to u = +0.443tt and 
Q_ to u = —0.44377. The sin 6 — sin 6 term in the expression for u can be written 69 

sin 6 - sin O = sin (0 - O ) cos O - [1 - cos (0 - O )] sin O (7.37) 
The second term on the right-hand side of Eq. (7.37) can be neglected when O is small 
(beam is near broadside), so that 

sin - sin 6 s» sin (0 - O ) cos O (7.38) 

Using the above approximation, the two angles corresponding to the 3-db points of the 
antenna pattern are ^ p 443A Q.443A 

0+ " 0o = Sm N</cos0 o ~N<icos0 o 

. _, -0.443A -0.443A 

a = sin ?& 

Nd cos O Nd cos 6 

The half-power beamwidth is 

6 B = + - 0. ~ -^- (7-39) 

B + Nd cos 6 n 

Therefore, when the beam is positioned an angle O off broadside, the beamwidth in the 
plane of scan increases as (cos O ) _1 . 



300 Introduction to Radar Systems [Sec. 7.7 

The change in beamwidth with angle O as derived above is not valid when the antenna 
beam is too far removed from broadside. It certainly does not apply when the energy 
is radiated in the endfire direction. 

A more exact expression for the beamwidth [obtained without the approximation of 
Eq. (7.38)] is 



e B = sin 1 ^0.443 — + sin 6U + sin" 1 (o.443 — - sin O ) (7 



40) 



6o=0 




Fig. 7.35. Radiation pattern 
of an array in free space 
showing beams at 6 = d and 



Care must be taken in the interpretation of Eq. (7.40) when the argument of the first 
sin 1 term is greater than unity, since a value of the sine greater than unity has no 

meaning. The antenna actually produces two beams, 
one of which is at an angle 6 , the other at the angle 
77 — O (Fig. 7.35). This follows from the fact that 
sin = sin (tt — 0). Therefore, as O approaches 90° 
(the endfire condition), the two beams overlap. If the 
antenna elements are in free space, both beams exist and 
merge to form the endfire beam at O = 90°. If the 
array is above a reflecting or an absorbing ground plane, 
the antenna cannot radiate at angles greater than 90° 
and the antenna pattern must be modified accordingly. 
The angle 0' defining the boundary between the endfire 
and the broadside regions is that value of O which 
makes the argument of the first sin- 1 term of Eq. (7.35) 
unity, or sin 0' = 1 - 0.443(A/AW). 
The above analysis applies to the linear array. Bick- 
„ _ „ . „„. more has shown that a similar result applies to a planar 

aperture ; 69 that is, the beamwidth in the plane of the scan 
varies approximately inversely as cos O , provided certain assumptions are fulfilled. 

Although the effect of scanning is to broaden the beamwidth in the plane of the scan, 
it cannot be concluded that the gain of the antenna always decreases in a similar fashion! 
Equation (7.36) for the linear array, or a similar expression for the planar array, shows 
that the maximum value of the gain or the field intensity is independent of the scan 
angle. The broadening of the beam is a direct consequence of the fact that the maxi- 
mum gain remains constant. The preceding statement is not readily obvious from an 
examination of the pattern in two dimensions since the antenna radiation pattern is 
three-dimensional. (Schelkunoff and Friis 64 prove that the directive gains of contin- 
uous linear antennas in the limiting cases of broadside and endfire radiation are equal 
to 4a/ A, where a is the antenna length, assumed large compared with the wavelength 1) 
In a practical array, however, the gain will change with scan angle because of changes 
in the mutual coupling between elements. The gain of an antenna will also vary with 
scan angle in a manner determined by the pattern of the element within the arrav 
[Eq. (7.33)]. y 

An interesting technique for graphically portraying the variation of the beam shape 
with scan angle has been described by Von Aulock, 70 an example of which is shown in 
Fig. 7.36. The antenna radiation pattern is plotted in spherical coordinates as a 
function of the two direction cosines, cos a„ and cos a„, of the radius vector specifying 
the point of observation. The angle <f> is measured from the cos ol x axis, and is 
measured from the axis perpendicular to the cos a x and cos a v axes. In Fig. 7.36, <f> is 
taken to be a constant value of 90° and the beam is scanned in the coordinate. ' At 
0=0 (beam broadside to the array) a symmetrical pencil beam of half-power width B 
is assumed. The shape of the beam at the other angular positions is the projection of 
the circular beam shape on the surface of the unit sphere. It can be seen that as the 



Sec. 7.7] Antennas 301 

beam is scanned in the d direction, it broadens in that direction, but is constant in 
the cf> direction. For 0^0, the beam shape is not symmetrical about the center of 
the beam, but is eccentric. Thus the beam direction is slightly different from that 
computed by standard formulas. In addition to the changes in the shape of the main 
beam, the sidelobes also change in appearance and position. 

Beam-forming Array. The inherent flexibility of the array antenna permits a 
number of beams to be generated simultaneously from the same aperture. Thus a 




Fig. 7.36. Beamwidth and eccentricity of the scanned beam. {From Von Aulock,'"' courtesy Proc. 
IRE.) 

single receiving antenna can be made to look in all directions at once, within the 
limitation imposed by the radiation pattern of the antenna elements. The ability to 
form many beams is usually easier on reception than transmission. This is not 
necessarily a disadvantage since it is a useful method of operating an array in many 
systems applications. Therefore the beam-forming array will be discussed primarily 
as a receiving antenna. 

The simple linear array which generates a single beam can be converted to a multiple- 
beam antenna by attaching additional phase shifters to the output of each element. 
Each beam to be formed requires one additional phase shifter, as shown in Fig. 7.37. 
The simple array in this figure is shown with but three elements, each with three sets of 
phase shifters. One set of phase shifters produces a beam-directed broadside to the 
array (6 = 0). Another set of three phase shifters generates a beam in the d = +0 O 
direction. The third set of phase shifters generates a beam in the direction = — 6 . 
The angle 6 is determined by the relationship O = sin" 1 (^Xjl-nd), where A<£ is the 
phase difference inserted between adjacent elements. Amplifiers may be placed be- 
tween the individual antenna elements and the beam-forming (phase-shifting) networks 
to amplify the incoming signal and compensate for any losses in the beam-forming 
networks. Low-noise amplifiers should be used if the signal-to-noise ratio is to be 
maximized. The output of each amplifier is subdivided into a number of independent 
signals which are individually processed as if they were from separate receivers. 

When beams are formed in networks placed after the RF amplifiers the antenna is 
called a postamplification beam-forming array, abbreviated PABFA. The beam- 
forming networks may be at either RF or IF. The circuitry (not shown) which follows 



302 Introduction to Radar Systems 



[Sec. 7.7 




Til 



Beam Beam Beam 
No. 3 No.2 No.1 

Fig. 7.37. Simultaneous postamplifier beam formation using array antenna, <h = constant pha 

|0i — 9o\ = |A0| = |277(rf/A)sin 0„|. r 








7 

1 






7 


f^ 


^ 


7 
1 




1 — I r 


Mixer 


(^ 


Mixer 


Mixer 




L0 


. 1 










> 


' 






> 






■ 








Toppe 


\An 

i 1 


no/ 


o 

o 


no/ 


\Amp/ 


, Beam 
No.t 

_». Beam 


lines c 

o 
o 






o 

o 

o 










No.2 

. Beam 
No. 3 



F[G. 7.38. Beam-forming network using tapped delay lines at IF. 



Sec. 7.7] Antennas 

the summing networks in Fig. 7.37 is conventional radar receivers. 



303 



The indicator 
display for a PABF A is slightly different from that of the usual radar. The output of a 
PABFA radar can be applied directly to a data-processing device without first being 
displayed to an operator. 

A convenient method of obtaining a receiving beam-forming network at IF is with 
the use of a series of tapped delay lines as illustrated in Fig. 7.38. The tapped delay 
lines are shown at IF. The phase of the IF is the same as that of the RF since phase is 

Crossed-line 
directional coupler 

>^ 

Waveguide 




Fig. 7.39. RF beam-forming network using tapped transmission lines. 

preserved during a frequency translation (except for the constant phase shift introduced 
by the local oscillator). 

The RF. beam-forming principle shown in Fig. 7.39 is used in the AHSR-1 height 
finder (Fig. 10.3) built by the Maxson Corporation for the Federal Aviation Agency. 
The waveguide transmission lines act as the delay lines. Energy is tapped from each 
waveguide at the appropriate points by directional couplers to form beams at various 
elevation angles. Considerable waveguide is used in arrays of this type. The Maxson 
height finder used 30 miles of 5-band waveguide to produce 333 beams. 

Another RF beam-forming device is the parallel-fed network attributed to 
Butler. 185 " 188 By properly utilizing 3-db directional couplers or hybrid junctions, with 
fixed phase shifters, it is possible to form n overlapping beams with an ^-element array. 
The Mubis 189 antenna, which uses a parallel-plate lens, and the Bootlace 190 antenna, 
which is a form of parasitic array lens, are also capable of RF beam forming. The 
Butler, Maxson, Mubis, and the Bootlace beam-forming devices are passive and there- 
fore can be used for both transmission and reception. 

The Luneberg lens can be used as a beam-forming network to form multiple beams 
in conjunction with a circular or a spherical array. 71 In this capacity it acts as an 
analog computer which automatically gives the correct phase relationships for the 
spherical array. The Luneberg lens can also be used, of course, to generate multiple 
beams directly, as described in Sec. 7.6. 

Signal-to-noise Ratio. The signal-to-noise ratio at the output of the summing 



304 Introduction to Radar Systems [Sec. 7.7 

network is theoretically the same as that of a conventional radar using a single large 
antenna to produce the same antenna beam. There need be no loss in the signal-to- 
noise ratio due to the forming of the beams in an array antenna, provided the array and 
its circuitry are properly designed. The amplifiers must have sufficient gain to over- 
come any losses in the beam-forming networks. Noise components from parts of 
the receiver other than the RF amplifier should be kept small. Since the signal com- 
ponents are added coherently in the summing networks of the array, while the noise 
components are added incoherently, there is, in principle, no loss as compared with a 
single-channel radar. The above explanation is qualitative and does not constitute 
a proof. A mathematical proof of the equivalence of the signal-to-noise ratio of a 
PABFA and a conventional radar was given by Rush. 72 

Comparison of PABFA with Scanning-beam Radar. In principle, a radar with a 
postamplification beam-forming array is equivalent in over-all performance to a radar 
with a single scanning beam, provided the comparison is made on a similar basis and 
that the received signals are processed in the optimum manner in each case. For 
purposes of comparison, let it be assumed that the PABFA radar consists of a receiving 
array generating a number of overlapping narrow beams fixed in space. The separate 
transmitting array is assumed to generate a single broad beam illuminating the same 
volume of space as covered by the multitude of receiving beams. For example, the 
receiving antenna might generate one hundred and eighty 1° pencil beams arranged to 
cover an angular sector 90° in azimuth and 2° in elevation. The transmitting pattern 
is therefore a single fan beam 90 by 2°. The single broad transmitting beam and the 
many narrow receiving beams are fixed in space, and the composite effect is that of 
many fixed radar beams operating in parallel. 

A scanning radar with a single narrow beam must cover the volume by time sharing. 
In the above example, a single 1 by 1° transmitting and receiving pencil beam would 
cover the 90 by 2° volume by making an observation in each of the angular resolution 
cells in sequence. 

The receiving antennas of the PABFA and the scanning radar are assumed to be of 
the same effective area, but the gain of the transmitting antenna used with PABFA is 
less than that of the scanning array since it has a considerably broader beam. Therefore 
the signal-to-noise ratio of each received pulse will be less with the PABFA radar than 
with the radar which uses a single scanning beam. However, this is compensated by 
the fact that the fixed receiving beams of the PABFA receive many more pulses per unit 
time from a target than does a scanning time-shared beam. It can be readily shown 
that the total energy contained in the many small pulses from the PABFA radar is the 
same as the total energy contained in the few large pulses received from a scanning 
single-beam radar, all other factors being equal. Therefore, if the energy available in 
the received signals is processed properly in both cases, the detection capability will be 
the same and the performance of the two radars will be equivalent. 

In practice, the two radars may not be exactly equivalent because it may not always 
be convenient or possible to process the signals in an optimum manner in both cases. 
The n pulses of small signal-to-noise ratio obtained in the PABFA must be integrated 
before detection (coherent integration) if the total signal-to-noise ratio is to be equal to 
n times the signal-to-noise ratio of a single pulse. Coherent integration is not always 
practical. Postdetection, or noncoherent, integration is more often used. Because of 
the nonlinear effects of the second detector, the total signal-to-noise ratio with post- 
detection integration is less than n times the signal-to-noise ratio of a single pulse and 
there is an integration loss (Sec. 2.6). The smaller the signal-to-noise ratio per pulse, 
the greater the integration loss. The individual pulses obtained with the scanning- 
beam radar are of larger signal-to-noise ratio than those obtained with the PABFA 
radar. There are fewer of them, making the total integration loss less with the 



Sec. 7.7] 



Antennas 



305 



scanning-beam radar. Therefore the PABFA radar may be slightly less efficient 
than the scanning-beam radar when the integration is performed noncoherently. 

The data rate of the two radars can be shown to be the same for equivalent detection 
capability, assuming ideal coherent integration. The data rate of the scanning-beam 
radar is the time taken by the beam to cover the entire volume and return to the same 
resolution cell. The scanning radar views the target but once during the scan time, 
while the PABFA radar with its fixed beams views the target continuously. Only one 
detection decision is made by the PABFA radar in this time since it must integrate all 
the available energy in order to equal the energy received by the scanning radar on a 
single observation. 



. ^ -/V \ > I > / V \ * 1 > / f \ » 1 > / >V 



(a) 



V 



—* -/j \ * * * / -9\ 



i i 



ib) 






Fig. 7.40. Arrangements for applying phase relationships in an array, (a) Series array, fed from one 
end; (6) series array, center-fed; (c) parallel-fed array with power-dividing network. 

Series vs. Parallel Feeds. The relative phase shift between adjacent elements of the 
array must be ef> = 2ir(d/X) sin 6 in order to position the main beam of the radiation 
pattern at an angle d . The necessary phase relationships between the elements may 
be obtained with either a series-fed or a parallel-fed arrangement. In the series-fed 
arrangement, the energy may be transmitted from one end of the line (Fig. 7.40a), or it 
may be fed from the center out to each end (Fig. 7.406). The adjacent elements are 
connected by a phase shifter with phase shift <f>. All the phase shifters are identical and 
introduce the same amount of phase shift, which is less than 2-rr radians. 

In the parallel-fed array of Fig. 7.40c, the energy to be radiated is divided between the 
elements by a power splitter. Equal lengths of line transmit the energy to each element 
so that no unwanted phase differences are introduced by the lines themselves. The 
proper phase change is introduced by the phase shifters in each of the lines feeding the 
element. When the phase of the first element is taken as the reference, the phase shifts 
required in the succeeding elements are <f>, 2<f>, 3<f>, . . . ,(N — \)<f>. 

The maximum phase change required of each phase shifter in the parallel-fed array 
is many times 277 radians. Because phase shift is periodic with period 2n, it is possible 



306 Introduction to Radar Systems [Sec. 7.7 

in some applications to use a phase shifter with a maximum of but 2tt radians. How- 
ever, if the pulse width is short compared with the antenna response time (if the signal 
bandwidth is large compared with the antenna bandwidth), the system response may be 
degraded. For example, if the energy were to arrive in a direction other than broadside, 
the entire array would not be excited simultaneously. The combined outputs from 
the parallel-fed elements will fail to coincide or overlap, and the received pulse will be 
smeared. This situation may be relieved by replacing the 277 modulo phase shifters 
with delay lines. 

A similar phenomenon occurs in the series-fed array when the energy is radiated or 
received at or near the broadside direction. If a short pulse is applied at one end of a 
series-fed transmitting array, radiation of energy by the first element might be completed 
before the remainder of the energy reaches the last element. On reception, the effect 
is to smear or distort the echo pulse. It is possible to compensate for the delay in the 
series-fed array and avoid distortion of the main beam when the signal spectrum is wide 
by the insertion of individual delay lines of the proper length in series with the radiating 
elements. 73 

In a series-fed array containing n phase shifters, the signal suffers the insertion loss 
of a single phase shifter n times. In a parallel-fed array the insertion loss of the phase 
shifter is introduced but once. Hence the phase shifter in a series-fed array must be 
of lower loss compared with that in a parallel-fed array. If the series phase shifters are 
too lossy, amplifiers can be inserted in each element to compensate for the signal 
attenuation. 

Since each phase shifter in the series-fed linear array of Fig. 7.40a has the same value 
of phase shift, only a single control signal is needed to steer the beam. The A^-element 
parallel-fed linear array similar to that of Fig. 7.40c requires a separate control signal 
for each phase shifter, or N — 1 total (one phase shifter is always zero). A two- 
dimensional parallel-fed array of MN elements requires M + N — 2 separate control 
signals. The two-dimensional series-fed array requires but two control signals. 

Thus the series-fed array introduces more loss than a parallel-fed array, but it is 
easier to program the necessary phase shifts. Neither feeding arrangement, however, 
seems unequivocally to excel the other in all situations. The final choice between the 
two will usually depend upon the system application. 

Resonant and Nonresonant Series-fed Arrays. Series-fed arrays radiating in the 
broadside direction may be classed as either resonant or nonresonant. A resonant 
array is one in which the elements are spaced exactly one-half wavelength apart. It 
radiates a beam normal to the array, and its impedance is well matched at the design 
frequency. The impedance match is obtained not only by choosing the impedances of 
the elements properly, but by adjusting a short-circuiting plunger at the end of the 
array. The short dissipates no power. Since the elements are spaced a half wave 
apart, any energy reflected by the short circuit is radiated as a beam normal to the 
array, just as is the energy propagated in the forward direction. It can be shown that 
all the elements of the resonant array couple equal power from the waveguide or trans- 
mission line and that there is no attenuation in a line loaded with pure series or pure 
shunt elements spaced at half-wavelength intervals. 1 Hence the aperture is uniformly 
illuminated. 

The chief limitation of the resonant array is its very narrow bandwidth. If the 
operating frequency is changed from the design frequency, the spacing between the 
elements is no longer a half wavelength, the impedance contributions of the elements do 
not all add at the input, and the array is not properly matched. The radiation pattern 
and the impedance of the array deteriorate with a change in frequency. In addition, 
the array is no longer uniformly illuminated and the radiated beam is not perfectly 
normal to the array. The usable bandwidth of a resonant array of N elements is 



Antennas 



307 



To arroy elements 



Open 

transmission 
nes», 




^Contacts to 
transmission line 



Sec. 7.7] 

approximately ± 50/ N per cent. 5 Therefore practical resonant arrays cannot be 
made too long. Small variations in the element spacings have a similar effect on a 
resonant array as a change in frequency. 

The limited-bandwidth restriction of a resonant array can be removed by making the 
spacing between the elements differ from a half wavelength. An array of this type is 
called nonresonant. Although the nonresonant array eliminates the poor impedance 
match and improves the bandwidth, it introduces other problems. The radiated beam 
is not normal to the array. In some cases 
this might prove to be a limitation, but it is 
the type of problem which can be tolerated 
in most applications. 

In the nonresonant array there must be no 
power reflected from the end of the array 
after the energy in the transmission line 
has passed the last element. Any reflected 
energy will radiate from the antenna as an 
undesired lobe at an angle —6, if the original 
wave radiates at an angle +6. The power 
at the end of the array must therefore be 
dissipated in a matched load. Ordinarily 
about 5 per cent of the total power gets 
beyond the last element and is dissipated as 
heat. 

Even with these limitations, the nonreso- 
nant array is useful, especially when the 
narrow bandwidth of the resonant array 
cannot be tolerated. 

Phase-shifting Devices. There are any 
number of devices which can provide the proper phase shifts at the elements of an 
array. They may be classed as (1) fixed phase shifters, (2) variable phase shifters 
actuated by mechanical means, and (3) variable phase shifters controlled by electronic 
means. 

One of the simplest methods of obtaining a fixed phase shift is with a length of trans- 
mission line. Fixed phase shifts are utilized in array antennas which generate fixed 
beams, as, for example, the postamplification beam-forming array described previously. 

Variable-phase-shift devices are based on changing the electrical length of a trans- 
mission line. The electrical length may be changed by physically shortening or 
lengthening the line. Most mechanical phase shifters are based on this principle. 
Electronic phase shifters operate by changing the (electrical) length of line by electronic 
means. 

One of the simplest forms of mechanical phase shifters is a transmission line designed 
with a telescopic section whose length can be varied. This is called a line stretcher. 
The telescoping section may be in the shape of a U, and the total length of line is changed 
in a manner similar to a slide trombone. 

Another phase shifter which has been used in array radar is the rotating-arm mechani- 
cal phase shifter (Fig. 7.41). 65 - 74 It consists of a number of concentric transmission 
lines. Each line is a three-sided square trough with an insulated conductor passing 
down the middle. (Details of the line are not shown.) A moving arm makes contact 
with each circular assembly. The arms are rotated to produce a continuous and 
uniform variation of phase across the elements of the array. When the phase at one 
end of the concentric line is increasing, the phase at the other end is decreasing. Hence 
one line can supply the necessary phase variation to two elements, one on either side of 



Fig. 7.41. Principle of rotating-arm mechan- 
ical phase shifter. 



308 



Introduction to Radar Systems 



[Sec. 7.7 



array center. A total of N/2 concentric rings are required for a linear array of N + I 
elements. The progressively greater phase variation required at the outer elements of 
the array as compared with the phase variation at the inner elements is readily obtained 
with the concentric-ring configuration. The outer rings, being larger, feed the outer 
elements of the array, while the inner rings feed the inner elements. The rotating-arm 
phase shifter has been used in a VHF height-finder radar 75 and in the Air Force Cam- 
bridge Research Center VHF experimental scanning radar called Billboard. 74 

A change in phase in a waveguide transmission line may be obtained by changing the 
dimensions of the guide. The wavelength of the radiation propagated in the guide is 




2* 



69 



Concentric coupled 
helix sections 



Fig. 7.42. Schematic representation of helical-line trombone phase shifter. 

dependent on the guide width. Several phase-shifting devices have been based on this 
principle. 5 ' 76 This technique has been applied to ground-controlled-approach (GCA) 
scanning radar 77 and to the AN/APQ-7 (Eagle) scanner. 78 

A mechanical device which gives more phase shift for a given amount of motion than 
a conventional line stretcher is the helical-line phase shifter due to Stark. 79 - 80 A 
schematic representation is shown in Fig. 7.42. Two helical lines 1-4 and 5-8 are 
coupled electromagnetically to one another by the helices 2-3 and 6-7. Each of the 
short coupled helices behaves as a directional coupler which transfers all the power 

from or to the main helix. A signal incident 
at terminal 1 is completely transferred to ter- 
minal 3. Terminals 2 and 4 are not excited 
in the process. The signal crosses the bridge 
to terminal 7 and is completely transferred to 
terminal 5. Likewise, terminals 6 and 8 are 
not excited. The helical-line phase shifter acts 
as a trombone line stretcher for a signal prop- 
agated from terminal 1 to terminal 5. The 
path length, and hence the phase shift, through 
the device is varied by mechanically position- 
ing the coupled helices. Since terminals 4, 2, 
6, and 8 are not excited by the signal travel- 
ing from terminals 1 to 5, a complementary phase shifter may be had by bridging ter- 
minals 2 and 6 and passing the second signal from terminal 4 to terminal 8. 

The phase velocity on the helical transmission line is considerably less than the 
velocity of light. For this reason a given mechanical motion produces more phase 
change than would a line stretcher in conventional transmission line. Thus a shorter 
phase shifter can be had which is especially advantageous at VHF or UHF frequencies. 
The reduction in length is essentially equal to the wind-up factor of the helix, which is 
the ratio of the circumference to the pitch. Wind-up factors may range from 10 to 20 
in practical designs. 79 




Fixed 
section 



Fig. 7.43. Principle of the rotary-waveguide 
phase shifter. 



Sec. 7.7] Antennas 309 

Another mechanical shifter is the rotary-waveguide phase shifter based on the 
properties of circularly polarized waves in round waveguide. The rotary-waveguide 
phase shifter has been described in detail by Fox 81 and was applied in the Bell Telephone 
Laboratories' FH MUSA scanning radar. 76 The rotary-waveguide phase shifter 
consists of three sections of round waveguide (Fig. 7.43). Sections I and III are fixed, 
while section II is free to rotate. Transition sections (not shown) might be employed 
to convert from rectangular waveguide to the round waveguide of section I and to 
convert the round waveguide of section III back to rectangular. Sections I and III are 
equivalent to quarter-wave plates. They convert linearly polarized waves into 
circularly polarized waves, and vice versa. Fox calls these 90° differential-phase-shift 
sections since the phase velocity of the polarization component in a particular plane is 
speeded up by 90° with respect to the polarization component in the orthogonal plane. 
The signal enters section I as a linearly polarized wave and is converted to a circularly 
polarized wave. Section II acts as a half-wave plate, or a 180° differential-phase-shift 
section. A rotation by an angle 6 results in a 20-radian change in the time phase of the 
output signal. An interesting property of the 180° section is that it converts circular 
polarization to the opposite sense of rotation. The phase-shifted circularly polarized 
wave is converted back to a linearly polarized wave by the action of the quarter-wave 
plate of section III. 

A phase shifter of this type is simple and compact and has little attenuation. The 
phase shift is obtained by the rotation of a round waveguide and can be made quite 
rapid. The mechanically rotating section II may be replaced by a ferrite Faraday 
rotator to produce an electronically controlled phase shifter with no mechanical 
moving parts. 82 ' 83 

A hybrid junction such as a magic T or its equivalent may be operated as a microwave 
phase shifter by placing mechanically adjustable short circuits in the collinear arms. 84 

A different form of mechanical beam steering is used in an array with spiral antenna 
elements. 85 - 86 The linearly polarized beam radiated by a flat, two-dimensional array 
of spirals may be scanned by rotating the individual spiral antenna elements. One 
degree of mechanical rotation corresponds to a phase change of one electrical degree. 
No additional phase-shifting devices are required. An array of spiral elements makes 
a simple scanning antenna. It is primarily useful in those applications where a broad- 
band element is required and the power is not too high. The entire assembly, including 
the spiral radiators and feed networks, but possibly excluding the rotary joint, can be 
manufactured with printed circuit techniques. Helical radiating elements have also 
been used in arrays to obtain phase shifts by rotation of the elements. 87 

All the phase shifters described above were mechanically actuated. The switching 
time required to position the phase shifter through a phase change of 360° depends on 
the type of phase shifter and its design. Switching times on the order of 0.1 sec or 
better are readily achieved with mechanical devices. Although these speeds permit 
antenna beams to be scanned considerably faster than is possible with a large antenna 
which must be positioned mechanically, even shorter switching times can be had with 
electronically controlled phase shifters. Switching times on the order of milliseconds 
are commonplace with most electronic shifters. Some devices are capable of micro- 
second switching times or better. 

An electronically controlled phase shifter at microwave frequencies may be obtained 
with ferrite materials, gaseous discharges, or traveling-wave tubes. 88 A ferrite phase 
shifter is a two-port RF transmission line in which the phase of the output signal is 
varied by changing the d-c magnetic field in which the ferrite is immersed. 89 Phase 
shifts of 360° can be obtained in a structure of relatively small size with magnetic fields 
of 100 oersteds or less and with insertion loss less than 1 db. Peak powers of several 
kilowatts are possible, and switching times can be made as short as tens of microseconds. 



310 Introduction to Radar Systems [Sec. 7.7 

Ferrite devices are sensitive to temperature changes and hysteresis effects. The 
development of better materials might relieve this problem, or the device might be 
operated in a temperature-controlled environment. 90 The inconvenience of a tempera- 
ture-controlled environment may be eliminated with a feedback control loop about the 
ferrite phase shifter to precisely control the phase shift. 91 - 92 Ferrite phase shifters are 
available from 10 Mc to millimeter wave frequencies. Ferroelectric phase shifters are 
also possible. 

Gaseous-discharge phase shifters are based upon the variation of the dielectric 
constant of the gaseous medium with the number of free electrons. The number of 
free electrons, and hence the phase, is a function of the current through the discharge. 93 
Gaseous-discharge phase shifters can handle about 1 kw of power and have fast 
switching time, ease of control, and large phase variation per wavelength and can be 
adapted to a wide range of frequencies. 88 They are limited, however, to relatively low 
peak powers, as are ferrite phase shifters. It is difficult to obtain stable operating 
characteristics with long life in sealed-off tubes. Furthermore, gaseous-discharge 
phase shifters are often noisy. 

The traveling-wave tube may be made to provide a fast, electronically controlled 
phase shift by variation of the helix voltage. Relatively little voltage variation is 
required to obtain the necessary phase shifts. In a particular tube, 360° of phase 
change was obtained for a change of 18 volts on the helix. 88 An advantage of the 
traveling-wave tube as phase shifter is that the same device can give amplification over a 
wide bandwidth and can provide a low-noise figure. The traveling-wave tube is not a 
bilateral device as are most of the devices mentioned. Separate phase-shifting cir- 
cuitry would therefore be required for transmitting and for receiving. 

Another method of obtaining an electronically controlled phase shift (due to Prof. 
W. H. Huggins of The Johns Hopkins University) is shown in Fig. 7.44. 71 > 94 > 95 A 
signal of frequency f , whose phase is to be shifted an amount <f>, is mixed with a control 
signal of frequency/,, in the first mixer. A portion of the control frequency is passed 
through a delay line of length r. The output of the delay line is a signal of frequency/ 
with a phase delay </> equal to 2-nf c T. The phase-shifted control signal and the output 
of the first mixer are heterodyned in the second mixer. If the sum frequency is selected 
from the first mixer, the difference frequency is selected from the second mixer. The 
result is a signal with the same frequency as the input signal f , but with the phase 
advanced by an amount <f>. If, on the other hand, the difference frequency were taken 
from the first mixer and the sum frequency from the second mixer, the output would 
be delayed in phase by the amount <f>. 

A phase shift may also be obtained by terminating a transmission line with a pure 
reactance. The energy incident upon the reactive termination is reflected with a phase 
change that is a function of the magnitude of the reactance. The reactive termination 
may be operated in a circuit such as a circulator or a properly phased balanced circuit 
to separate the incident and the reflected waves. -The phase shift through the device 
is varied by changing the reactance of the termination. One method of obtaining an 
electrically variable reactance is with the varactor (variable-capacitance) diode. 96 An 
example is shown in Fig. 7.45 in which two variable-capacitance diodes are coupled by 
a waveguide short-slot hybrid junction. (Coaxial and strip-line equivalents can also 
be used.) The signal input at arm 1 is divided equally between arms 2 and 3. (The 
phase of the energy transferred from one line to the other is advanced 90° in the short- 
slot coupler.) The two signals are reflected by the diodes with a change in phase 
depending on the value of capacitance and recombine in arm 4. The capacitance, and 
hence the phase shift, is controlled by the bias voltage applied to the diodes. Phase 
shifters based on this principle have been constructed at frequencies ranging from UHF 
to X band. The spreading resistance of the variable-capacitance diodes causes an RF 



Sec. 7.7] 



Antennas 311 



insertion loss of approximately 1 db. These phase shifters are compact, fast, and 
efficient, but are limited to low power levels and have limited phase shift-bandwidth 

product. 

Variable-capacitance diodes may also be used to switch fixed lengths of transmission 
lines as a discretely variable line stretcher. 191 . 192 The length of line that is switched 
determines the phase. A number of line lengths must be available m order to approxi- 
mate the needed increments of phase shift. The lines might be of binary lengths (1,2, 
4 8, etc., units) so that the phase shift can be controlled with digital-computer logic. 
Diode switching times can be of the order of microseconds or less, but the insertion 
loss with the switched transmission-line phase shifter is greater, generally, than the 
other RF phase shifters discussed. Ferrites or gas tubes can also be used as switches 
with this type of shifter. Because the available phase shifts are discrete rather than 
continuous, spurious lobes can appear in the antenna radiation pattern. If the quanti- 
zation level is sufficiently small, these spurious lobes are negligible. For example, if 
the phase shift is quantized into four bits (smallest increment 22.5°) the antenna gain 
is reduced approximately 0.1 db and the largest spurious lobe is about 24 db below the 
main beam. 



© 



1st 




fo + fc . 




2d 


f Q & t 


mixer 




mixer 
























Delay 

T 












f 


. / 


* 



Variable-capacitance 
diode termination 




Fig. 7.44. Schematic representation of the 
Huggins electronic phase shifter. 



Output© 
Input © 



Short-slot Variable-capacitance 

hybrid junction diode termination 

Fig. 7.45. A variable-capacitance diode 
phase shifter using a short-slot hybrid 
junction. 



A phase shift may also be obtained with amplitude adjustments only. An antenna 
consisting of elements spaced one-quarter wavelength apart with alternate elements in 
phase quadrature can be made to steer its beam by varying the amplitude at each 
element. 97 No phase shifters in the conventional sense are required. 

Still another approach to the design of a steerable array is by controlling the coupling 
of slot radiators. 98 ' 99 Normally, in an array made by cutting slots in the side of a 
waveguide, the amplitude and phase of the energy coupled from the slots are fixed. 
However, the slot radiation can be controlled by means of discontinuities, such as stubs 
or irises, judiciously placed within the waveguide near the slot. Irises, for example, can 
be designed to be mechanically positioned by means external to the guide. Changes in 
iris position change the amount of coupling and the phase. Ferrite discontinuities 
within the guide can be made to electronically control the amplitude and phase of the 
radiation coupled from the slot. Variations in coupling are obtained by varying the 
d-c magnetic field applied to the ferrite with an external electromagnet. 

Frequency Scanning. A change in relative phase between adjacent elements may be 
obtained by a change in frequency. This principle can be used to scan a beam from an 
array if the phase shifters are frequency-dependent. A frequency-scanned antenna 
might be represented by the series-fed array shown in Fig. 7.40a with fixed lengths of 
transmission line connecting the elements. The total phase through a fixed length / of 
transmission line is lirfl/c, and thus is a function of the frequency/. The lines connect- 
ing adjacent elements of the series-fed frequency-scanned array are of equal length and 
chosen so that the phase at each element is the same when the frequency is the center 
frequency /„. When the frequency is exactly /„, the beam points straight ahead. As 



312 Introduction to Radar Systems [Sec. 7 7 

the frequency is increased above/ , the phase through each length of transmission line 
increases and the beam rotates to one side. At frequencies below f , the beam moves 
in the opposite direction. 

The implementation of a frequency-scanned-array radar is relatively straightforward 
in principle. The phase shifters are simple lengths of transmission line. Transmission 
lines can handle large power with low loss. They are reciprocal devices and may be 
used on transmission as well as on reception. The beam can be steered as rapidly as 
the frequency can be changed, provided the switching time is long compared with the 
time for the wave to transit the length of the array. 

Frequency scan is more appropriate for one-dimensional rather than two-dimensional 
scanning. Some other phase-shifting technique may be used in conjunction with 
frequency scan to steer in the other dimension. 

The simplicity of frequency scanning is complicated by the relatively large frequency 
spectrum which must be available in order to scan, the beam over a reasonable angular 
sector. The electromagnetic frequency spectrum is quite crowded, especially at the 



—$kr< 



~^p£^< '—A^r< —/\-< -VX: 




7" 



v* 3 V-^ 



\-^ 



'4v,V^ 



— Aa~ «3 



SSmilthf P ' anar Srray W ' th P hase " shift voIume tnc scan in two angular coordinates (elevation and 

lower radar frequencies, and systems which require wide bandwidths must justify the 
need. Even when the wide-frequency band is available, the use of the spectrum to 
accomplish frequency scanning may preclude the use of frequency for other purposes 
such as for electronic counter-countermeasures (ECCM), accurate range measurement' 
or resolution. 

Two-dimensional Scanning.™ The beam generated by a two-dimensional planar 
array may be scanned in space by applying to each element the necessary phase shift 
required to position the beam in the desired direction (Fig. 7.46). An independently 
controlled phase shifter is attached to each element. The proper phase is determined 
by superimposing the phase shifts needed to scan an angle 6 in the azimuth plane and 
0o m the elevation plane. If the antenna gain is high, the number of elements will be 
large and a large number of individual control signals are required to adjust all phase 
shifters to the correct value. For example, if the antenna beamwidth were 1° the array 
would consist of approximately 10,000 elements, arranged in a square with 100 elements 
on a side. A total of 10,000 control signals would be necessary if the phase of each 
element were controlled independently. 

It is possible to operate the array in such a manner that each phase shifter need not be 
controlled separately. A considerable saving in the number of control signals can be 



„ _ _i Antennas 313 

Sec. 7.7] 

had by steering the beam independently in azimuth and elevation (Fig. 7.47). An array 

of this type is called a parallel-parallel structure since the phasing networks m both scan 

planes are parallel-fed. All the elements which lie in the same column receive the 

identical phase shift in order to steer the beam in one plane. To steer the beam in the 

orthogonal plane, all the elements that lie along the same row also receive the same 

phase shift The elements in the same row may be considered as one unit lor purposes 

of control Likewise, the elements in the same column may beconsidered one control 

unit Applying the phase shifts by rows and by columns follows from the independence 

of radiation patterns in the principal planes as given by Eq. (7.34). A beam may be 

steered to any position within the coverage volume by selecting the proper horizontal 

(azimuth) displacement and the proper vertical (elevation) displacement. If, in the 



/^ /j^, ^^ 







I Input 

i A 

Azimuth controls 

Fig. 7.47. Volumetric scanning of a planar array with separate azimuth and elevation control signals 
(parallel-parallel structure). 

example of the previous paragraph, phase shifting were carried out by rows and columns, 
only 198 control signals would be needed instead of the 10,000 necessary when in- 
dependent controls were used. 

There are other combinations of series- and parallel-fed planar arrays which might 
be employed. 67 In the series-series planar array all series phase shifters in the elevation 
plane take the same value, as do all the series phase shifters in the azimuth plane. 
Therefore, only two control signals are required. 

A planar array using frequency scan in azimuth and phase shifters to scan in elevation 
is diagramed in Fig. 7.48. This is an example of a parallel-series array. The antenna 
may be considered as a number of frequency-scanned arrays placed side by side. 

The Frescan radar (Fig. 1.11) developed by Hughes Aircraft Co. uses an array in 
which steering in elevation is accomplished with frequency scan and steering in azimuth 
by mechanical rotation. An end-fed frequency-scanned 40-element linear array acts 
as a line-source feed for a parabolic-cylinder reflector. It is claimed that the beam can 
be scanned an angle of more than 100° in elevation with a frequency excursion of less 



314 Introduction to Radar Systems [ Sec 7 7 

than .10 per cent. In shipboard use, Frescan incorporates an electronic pitch-and-roll 
stabilization system that modifies the elevation and scanning pattern to compensate for 
ship s motion. r 

Array Elements. Almost any type of radiating element can be used as the building 
block of an array antenna. Detailed descriptions of the various radiators used for 
antennas may be found in the standard texts on antennas and will not be discussed here 
However, some of the radiating elements commonly found in arrays will be briefly 
mentioned. J J 

The dipole is a simple radiating element which has been widely employed with both 
mechanically scanned and electronically scanned arrays. Another simple element 
related to the dipole is the slot cut into the side of a waveguide. A slot array is easier to 
construct at the higher microwave frequencies than a dipole array. The power coupled 
out of the guide by the slot is a function of the angle at which the slot is cut. When slots 
or dipoles spaced half wavelengths along the walls of a waveguide are fed in a series 
lashion, the phase of the elements must be alternated along the array since the field 

V 



Variable 
frequency - 
signal 



Delay line 



Delay line 



V 



Delay line 



w 




T 









V 



T&r 



V 






v 



-A 



V 



Delay line - — • — 



V 



fn eievadon VOlUmetriC SCa " ning ° f a P lanar arra y usin g fre q uenc y «=an in azimuth and phase-shift scan 

!!£? ' ^f Chang6S phaSC by 18 °° in half a S uide wavelength. Alternating the 
phase of the elements causes the phase of the signal radiated from each element to be 

TJT°' T P J? a 1 radlatCd , by a Sl0t Can be Cha "g ed 1 80 ° b y tiltin g ^ in the opposite 
direction. In a dipole array the phase can be reversed by reversing the dipole 

The slot and the dipole produce a relatively broad radiation pattern and are used 
where large angular coverage with a single array is desired. When the required 
coverage is not too large, more directive elements can be used. Polyrods helices 
spira s- or logarithmically periodic-,- radiators have been ^^^J 
directive elements are desired. The last-mentioned element (as well as the spiral 
radiator) is capable of large bandwidths. wen as ine spiral 

naSrn 1 " wll" 8 den ? ents ° f array antennaS must not onl y have the proper radiation 
5E ' Tu T P u S bC , tWeen elementS muSt be smaII - 6? AIso > the element pattern 
nSt ff ade 6 n 8 Wh rl n plaC , ed m the P resence of the °thers because of scattering and 
diffraction effects." Those elements for which the mutual coupling is low, such as a 



q 7 71 Antennas 315 

directive polyrod, are usually physically large enough to cause significant pattern 
broadening due to diffraction by adjacent elements. 

Mutual coupling between the elements of an array causes the input impedance of a 
radiating element to be different from the impedance it would have if isolated in free 
space 103 - 106 Mutual coupling can be accounted for in the design of the array, but 
because it is a function of the scan angle, it may not always be practical to do so. Large 
mutual coupling between elements can result in a poor radiation pattern, a raised 
sidelobe level, and a mismatched array. In general, mutual coupling is not important 
in antennas with modest requirements on sidelobe-level or beam-position accuracy, 
but if extremely low sidelobes, or if precise positioning of the beam is desired, or if the 
scan angle is large, mutual-coupling effects must be considered. The advantages of 
precise aperture control which is characteristic of discrete-element arrays may be 
negated by mutual coupling. 107 

Unequally Spaced Arrays. The vast majority of array antennas have equal spacing 
between elements. Arrays with unequally spaced elements, however, have properties 
that might be of advantage in certain applications. 108 Two advantages claimed for 
unequally spaced arrays are that fewer elements can be used as compared with an 
equally spaced array of comparable beamwidth and that broadband operation is 

possible. . 

One method of obtaining an array with unequal spacing is to remove elements at 
random from an equally spaced array. More controlled techniques of a pseudo- 
random nature may be used, however, to prescribe the element spacings. The synthesis 
of optimum configurations is a difficult task. Most designs are based on trial and 
error. However, the unequally spaced array can be analyzed in terms of an equivalent 
uniformly spaced array, with a nonuniform amplitude distribution, whose pattern is 
the best mean-square representation for the unequally spaced array. 109 

The gain of an array is proportional to the number of elements it contains. Therefore 
"thinning out" by removing elements decreases the gain even though the beamwidth 
might remain essentially unchanged. If the beamwidth remains unchanged as ele- 
ments are removed in a thinned-out array, the average sidelobe level must increase to 
compensate for the decrease in gain. Spacing the elements of a thinned-out array 
unequally rather than equally (with a spacing greater than a half wavelength) tends to 
"smear" the undesired grating lobes that would otherwise be produced. 

An example of the radiation pattern of an unequally spaced linear array of 25 
elements is shown in Fig. 7.49. The abscissa Z is a universal pattern factor equal to 
M„inM)(sin - sin 6 ), where d min is the smallest of the unequal spacings, A is the 
wavelength, 6 is the angle measured from the normal to the array, and d is the angle to 
which the main beam is steered. Plotting the pattern in terms of Z permits it to be 
analyzed either as a function of frequency or of beam-steering angle. Also shown is 
an abscissa scale in degrees which applies to the case of 6 = and d min = 2A. The 
length of the array under these conditions is 1 00A. The closest element spacing in the 
antenna whose computed pattern is shown in Fig. 7.49 is at the center of the array. 
The spacings increase monotonically in a controlled manner outward from the array 
center. The element spacings are symmetrically placed with respect to center of the 
array consequently the radiation pattern is also symmetric about its axis. The 
radiation pattern is plotted on either side of the Z axis to show the relative phase 
relations between the various sidelobes. 

A 100A array with 200 elements spaced A/2 apart has a theoretical beamwidth of 
51°. The beamwidth of the 25-element thinned-out array of Fig. 7.49 is 0.65°. If 
the same 25 elements were equally spaced over a 100A aperture with 4A spacing, the 
beamwidth would be comparable with that obtained with a full aperture of 200 elements, 
but grating lobes would appear at B = ±14.5, ±30, ±48.5, and ±90°. 



316 Introduction to Radar Systems [Sec. 7.7 

It has also been shown that the sidelobe level of a nonuniformly spaced array with 
uniform excitation of the elements theoretically can be reduced in height to approxi- 
mately 2/N times the main-lobe level, where N is the number of elements, without 
increasing the beamwidth of the main lobe. 182 

The principle of unequally spaced thinned-out arrays has been applied to radio- 
astronomy telescopes to effect an over-all increase in economy without a significant 
decrease in beamwidth. 174 A linear array of 266 uneq ually spaced elements replaced a 
388 equally spaced element array. A 0.3° beam was obtained which could be scanned 
±30°. The element spacing was chosen to approximate a cosine-squared aperture 
illumination. This is an example of how unequal spacings can effect a "space taper" 




20 30 40 

S, deg, for d m \„ - 2X 



50 



60 



70 90 



0.2 



0.4 



J ' i i 



0.6 0.8 



1.0 1.2 



/= ^(sintf-sintfo) 



1.6 



1.8 



2.0 



Fig. 7.49. Computed radiation pattern of a 25-element unequally spaced array. {Courtesy Electronic 
Communications, Inc.) 

across the array aperture with the same approximate pattern properties (at least in the 
vicinity of the main lobe) as if an amplitude taper had been used. In transmitting 
applications space tapering permits a form of tapered aperture illumination with 
identical transmitting elements, each radiating the same power. 

Radar Applications of the Array. One important application of the array in radar 
has been as a fixed-beam antenna scanned by the mechanical rotation of the entire 
antenna structure. Large mechanically rotated array antennas are more competitive 
with other antenna types at the lower radar frequencies than at the higher microwave 
frequencies. At the lower frequencies only a relatively small number of antenna 
elements are needed to obtain an array with large receiving cross section. The mechani- 
cally scanned array has the advantage of a compact structure as compared with an 
equivalent reflector or lens antenna. The array can be made relatively flat, whereas 
the reflector antenna must have some depth in order to support a feed at a distance from 
the main part of the antenna. 



„_, Antennas 317 

Sec. 7.7] 

One of the early radars which used a mechanically rotated array antenna was the 

SCR-270 a ground-based surveillance radar operating at a frequency of 106 Mc. 

Its antenna was a planar array of dipoles arranged in four columns of eight elements 

each. The beamwidth was 28° in azimuth and 1 0° in elevation, and the entire structure 

rotated at 1 rpm. ... , , 

The compact size of an array makes it an attractive antenna for shipboard radar 
applications Byers and Katchky 111 describe a 12-ft-long rectangular-slotted- 
waveguide linear-array antenna consisting of 128 alternately inclined slots operating at 
X band The slotted waveguide is an especially desirable antenna because of its 
simplicity and compactness. To avoid resonant effects, the spacing between the slots 
was made slightly different from a half wavelength. The slots were alternately inclined 
to accommodate the 180° phase reversal which occurs in a waveguide transmission line 
every half wavelength. By making the array with nonresonant slot spacing, the beam 
pointed slightly to one side of the mechanical center of the array, but it was not con- 
sidered a limitation for the particular application for which the antenna was designed. 
A 30° flared horn was used in the vertical plane to obtain more directivity in elevation. 
The beamwidth was 0.7 by 16°. 

Another example of a rotating linear-array antenna for radar application was 
described by McCoy et al. 112 The antenna consisted of a linear array of 80 waveguide 
horns The frequency of operation was 5-band, and the length of the array was 20 ft. 
The waveguide horn elements were fed by a complex network of waveguide and rigid 
coaxial-line power dividers. The antenna pattern was a 1 i by 30 fan beam. Sidelobes 
of 25 db or better over a 35 per cent bandwidth were reported. 

The first application of a stationary array antenna which steered the beam with 
mechanical phase shifters was developed by the Bell Telephone Laboratories for 
short-wave radio reception in the early 1930s. 113 The array was given the name MUSA 
which stood for multiple-unit steerable antenna. Six rhombic antennas extending f 
mile in length generated a 2.5° endfire beamwidth at a wavelength of 16 m and could be 
scanned between 12 and 23° elevation angle by the phase shifters. The array was later 
increased to 16 rhombics extending 2 miles with a beamwidth less than 1 . 

The MUSA beam-steering technique was applied during World War II in a micro- 
wave radar called FH MUSA. 115 - 116 The antenna was an array of 42 polyrod elements 
arranged in three horizontal rows of 14 elements each. Each of the three elements in a 
vertical column was fed in phase so as to provide more directivity in the vertical plane 
than would be obtained with one element alone. No beam steering was applied in the 
vertical plane ; hence the antenna was basically a 14-element linear array. The beam 
was scanned in the horizontal plane with rotary-waveguide phase shifters. 

The polyrod elements were spaced 2 wavelengths apart in the horizontal dimension 
and 2 68 wavelengths in the vertical dimension. If omnidirectional elements were used 
in an array with this spacing, grating lobes would appear and give ambiguous angle 
measurements. For example, elements spaced 2 wavelengths produce grating lobes at 
+ 30 and ±90° These grating lobes may be removed with directive elements that 
radiate little or no energy in the direction of the grating lobes. The disadvantage in 
reducing grating lobes in this manner is a restricted angle of scan. In the FH MUbA 
antenna! the directive polyrod elements each had a gain of 16.4 db The radiation 
pattern of the polyrods permitted a scanning range of ±9 with sidelobes 12 db down. 
The total gain of the antenna was 29 db. 

The FH MUSA radar operated at S band and was used for fire-control purposes 
aboard large Navy ships. The antenna was 1 ft in length and generated a fan beam 2 
in the horizontal direction by 6.5° in the vertical direction. The rotary-waveguide 
phase shifters scanned the beam with a uniform motion at the rate of 10 scans per 
second. 



318 Introduction to Radar Systems t Sec 77 

Another electromechanically steerable antenna developed during World War II was 
the Eagle scanner used in the AN/APQ-7, a high-resolution Z-band, ground-mapping 
radar for navigation and bombing.*"."* The same scanning principle has also beef 
applied to ground-controlled-approach (GCA) radar." The Eagle scanner is a 16-ft 
linear array of 250 dipole radiators mounted with half-wavelength spacing on a wave- 
guide feed line. Since the phase reverses along the waveguide every half wavelength 
adjacent dipoles are reversed. Scanning of the beam is accomplished by mechanically 
moving one wall of the waveguide. A change in waveguide dimensions changes the 
phase velocity of the radiation along the guide and hence changes the phase between the 
dipoles. The motion of the scanning technique is reciprocating rather than rotary- 
consequently perfectly uniform beam scanning can only be approximated ' 

The beamwidth is 0.4 to 0.5° in azimuth and is shaped in elevation to give an approxi- 
mately cosecant-squared coverage down to 70° angle of depression. The beam can be 
made to scan a 60° azimuth sector in f sec. The basic Eagle mechanism is capable of 
scanning rates as high as 20 times per second. The beam is scanned through an angle 
of ±30 from the perpendicular to the array by alternately feeding the array from 
opposite ends. One scan is from -1 to +30°, while the next is from +1 to -30° 
As the beam scans through the perpendicular to the antenna, the array becomes 
resonant because of the half-wave spacing between elements. At resonance the VS WR 
becomes quite large. The large VSWR is used to place a mark on the cathode-ray-tube 
display to indicate the center of the scan and calibrate the position of zero degrees 

One of the major limitations of the Eagle scanner is the mechanical precision 
required in its construction. Even so, it has been successfully manufactured for use in 
operational radars, both airborne and ground-based. 

ESAR (Fig. 1.12) is an example of an electronically steerable array radar using a 
frequency-conversion phasing scheme. The antenna is 50 ft in diameter. The beam 
can be scanned in less than 20 //sec. A cluster of 25 scanning beams, five rows in 
elevation and five columns in azimuth, can be generated by the ESAR system A 
separate transmitter feeds each of the /.-band log-periodic antenna elements The 
array has provision for 8,768 elements. 

Electronic scanning techniques have been applied to acoustic arrays for sonar 
detection. - 1 9 There is close analogy between radar array techniques and acoustic 
arrays. 

Advantages and Limitations. The array antenna has the following characteristics 
not generally enjoyed by other antenna types : 

1. The beam from an array can be rapidly scanned over the coverage of the antenna 
without the necessity of moving the entire antenna structure. The beam may be 
scanned continuously or moved discretely from one point in space to any other point in 
space, Mechanically actuated phase shifters can scan the beam through its coverage 
as fast as 0. 1 sec or better, while electronically controlled phase shifters can scan a beam 
at rates many orders of magnitude greater. 

2. The array has the ability to generate simultaneously many independent beams 
from the same antenna aperture. The array might generate fixed beams, scanning 
beams or both at the same time. Simultaneous-lobing (monopulse) tracking beams 
can be formed, or a single beam might be programmed to generate conical-scan tracking 

3. Large peak and/or large average powers may be obtained with separate trans- 
mitters at each of the elements of the array. 

4. The steerable feature of an array means that the beam from a shipboard or airborne 
radar may be stabilized electronically rather than by mechanically moving large 

5. A particular aperture distribution may be more readily obtained with the array 
than with the lens or the reflector since the amplitude and phase of each element of the 



Sec. 7.7] Antennas 319 

array can be individually controlled. The ability to control the aperture distribution 
makes it theoretically possible to achieve an antenna with low sidelobes. 

6 Spillover loss is common in the reflector or lens antennas, but is absent in the 
arrav For this reason the efficiency of an array antenna can be slightly higher than 
that of other antennas, provided other losses characteristic only of the array, such as 
losses in the phase shifters or the beam-forming networks, do not negate any gain 
obtained from the absence of spillover. 

One of the disadvantages of the array antenna is the limited coverage available from a 
single plane aperture. Theoretically, a single plane aperture should be able to scan a 
complete hemisphere. However, this is seldom practical since the antenna beam 
shape changes with scan angle, but more importantly, the scan angle is limited by mutual 
coupling, by the radiation pattern of the elements that make up an array and by the 
Se to avoid grating lobes. Practical arrays might scan ±30° without much 
difficulty. Larger scan angles are, of course, possible. 

If wider coverage is necessary, it may be obtained with more than one aperture. 
The elements could conceivably be arranged on the surface of a sphere or a cylinder in 
order to obtain more complete coverage. However, not all the elements of the sphere 
can be used to generate a beam in a particular direction because of the self-shielding ot 

the spherical array itself. ... A r*u a 

Cost and complexity are perhaps the biggest limitations to the widespread use of the 

array antenna in radar applications. The cost of an array is roughly proportional o 

the number of elements. Hence the same beamwidth (gain) antenna will probably 

cost about the same at the lower frequencies as at the higher frequencies even though 

the lower-frequency antenna is larger and has more effective antenna area. Ihe 

lower-frequency antenna might even be cheaper than a similar one at higher frequency. 

The need to keep the number of elements to a reasonable value means that the array is 

not usually competitive in cost when high gains are required. The array antenna is 

probably more economical for radars operating in the VHF or the lower UHF bands 

than at the higher microwave frequencies. ,r, rw. i ™<>ntc 

An array which generates a 1° beamwidth requires approximately 10,000 elements, 

while an array with a 0.1° beamwidth requires almost 1 million elements, assuming 

that they are spaced a half wavelength apart. The performance of the many-element 

array will be degraded but little when even a relatively large number of elements tail. 

Thus the array antenna does not "die all at once," as might a conventional radar with a 

single beam. However, the life of the components is finite. If, for example, the 

average life of each element were 10,000 hr, a 1° beamwidth array would experience a 

failure at the average rate of one per hour. Although many such failures may be 

accumulated before the performance of the radar is significantly degraded, the failures 

must eventually be found and replaced. 

An important factor which contributes to the cost and complexity of an array is the 
need to maintain phase stability even under adverse operating conditions. In all the 
preceding analysis and discussion of array antennas it was assumed that the only phase 
changes were those deliberately and knowingly introduced by the radar designer. It 
is necessary that the phase of the transmission lines, amplifiers mixers, and other 
components used in the array be constant or negligibly small. In order to achieve 
this ideal, the environment in which the radar operates must be maintained at constant 
conditions and the voltages applied to the amplifiers must not vary. One approach 
to maintaining stable phase conditions is to use some sort of servo-controlled loop to 
maintain constant the phase shift through the major networks of the array. Markow 
describes a servo phase-control system which maintains the phase between the output 
and the input of a UHF amplifier to within 2° by comparing the phase of the amplifier 
output with that of the input in a phase-sensitive detector. 



320 Introduction to Radar Systems r SEC 7 8 

Even though the steerable array is often more costly and more complex than other 
antennas, it would undoubtedly be used where its high-speed beam-steering or multiple- 
beam-forming capability is needed and cannot be obtained by any other means 
However, the more or less conventional mechanically scanned antenna has been able to 
meet most of the requirements of radar. Although it cannot steer as rapidly as an 
electronically scanned array, it has been able to scan as fast as required for the majority 
of radar applications. Similar statements can be made for the property of forming 
multiple beams from the same aperture as well as for most of the other stated advantages 
of the array. & 

The array will be used when it can perform a function better and/or more cheaply 
than other competitive antennas. If the array is to compete economically its com- 
ponents must be cheap, reliable, and produced and assembled automatically Perhaps 
the most promising area for future component development is that of solid-state 
devices. The radar antenna of the future, or for that matter the radar system of the 
future, might well be an all-solid-state device. The radar systems engineer must await 
the efforts of the research scientist and the component-development engineer before the 
lull theoretical potentialities of large-array antennas can be economically exploited for 
general radar application. 

7.8. Pattern Synthesis 

The problem of pattern synthesis in antenna design is to find the proper distribution 
of current across a finite-width aperture so as to produce a radiation pattern which 
approximates the desired pattern under some condition of optimization. Pattern- 
synthesis methods may be divided into two classes, depending upon whether the aperture 
is continuous or discrete. The current distributions derived for continuous apertures 
may sometimes be used to approximate the discrete-aperture distributions and vice 
versa, when the number of elements of the discrete antenna is large. The discussion in 
this section applies, for the most part, to linear one-dimensional apertures or to rec- 
tangular apertures where the distribution is separable, that is, where A(x,y) = A(x)A(y). 

All pattern-synthesis methods are approximations since practical antennas must be 
of finite dimension. There is a further restriction in that aperture distributions which 
give rise to large reactive-power components are to be avoided. Large reactive 
power is characteristic of supergain antennas and results in excessive losses and narrow 
bandwidth (high 0. 64 . 121 

The synthesis techniques which apply to array antennas usually assume uniformly 
spaced isotropic elements. The element spacing is generally taken to be a half wave- 
length. If the elements were not isotropic but had a pattern E£6), and if the desired 
over-all pattern were denoted E a {6), the pattern to be found by synthesis using techniques 
derived for isotropic elements would be given E d (6)/E e (d). 

Fourier-integral Synthesis. The Fourier-integral relationship between the radiation 
pattern and the aperture distribution was discussed in Sec. 7.2. The distribution A(z) 
across a continuous aperture was given by Eq. (7.14). 

4(z) = - J_ E(4>) exp f -j2n * sin <f>) d(sin c/>) (7.14) 

where z = distance along aperture 

E(<f>) = radiation pattern 
If only that portion of the aperture distribution which extends over the finite-aperture 
dimension d were used, the resulting antenna pattern would be 

£„(<£) = J ^(z)exp (pTr^sin <f>\ dz (7.41) 



g 7 g-i Antennas 321 

Substituting Eq. (7.14) into the above and changing the variable of integration from 
to £ to avoid confusion, the antenna radiation pattern becomes 

£ o ($ = - [ m \ °° £(!) exp j2n - (sin <f> - sin |) d| dz (7.42) 

Interchanging the order of integration, the approximate antenna pattern is 

EM-IT EQ) si" WAXsM- sing)] d| (7 . 43) 

aW _ A J- oo W ^(d/AKsin <£ - sin f ) 

where £ (<£) is the Fourier-integral radiation pattern which approximates the desired 
radiation pattern £(<£) when A(z) is restricted to a finite aperture of dimension d. 

Ruze 121 has shown that the approximation to the antenna pattern derived on the 
basis of the Fourier integral for continuous antennas (or the Fourier-series method for 
discrete arrays) has the property that the mean-square deviation between the desired 
and the approximate patterns is a minimum. It is in this sense (least mean square) that 
the Fourier method is optimum. The larger the aperture (or the greater the number of 
elements in the array), the better will be the approximation. 

Whenever the desired antenna pattern has discontinuities or whenever the value ot 
the desired pattern changes rapidly, the Fourier method results in an oscillatory 
overshoot (Gibbs's phenomenon). The overshoot does not decrease in magnitude as 
the aperture is increased, but approaches a value of about 9 per cent of the total 
discontinuity. . 

The Fourier series may be used to synthesize the pattern of a discrete array, just as the 
Fourier integral may be used to synthesize the pattern of a continuous aperture. 122 
Similar conclusions apply. The Fourier-series method is restricted m practice to 
arrays with element spacing in the vicinity of a half wavelength. Closer spacing 
results in supergain arrays which are not practical. 126 . 127 Spacings larger than a 
wavelength produce undesired grating lobes. 

Woodward-Levinson Method. The least-square criterion of the Fourier-integral 
method is but one technique upon which antenna synthesis can be based. Another 
method of approximating the desired antenna pattern with a finite aperture distribution 
consists in reconstructing the antenna pattern from a finite number of sampled values. 
The principle is analogous to the sampling theorem of circuit theory in which a time 
waveform of limited bandwidth may be reconstructed from a finite number of samples. 
The antenna-synthesis technique based on sampled values was introduced by Levinson 
at the MIT Radiation Laboratory in the early forties and was apparently developed 
independently by Woodward in England. 5 ' 124 ' 125 . 

The classical sampling theorem of information theory as given by Shannon is: It a 
function f(t) contains no frequencies higher than Jfcps, it is completely determined by 
giving its ordinates at a series of points spaced 1/2 W seconds apart." The analogous 
sampling process applied to an antenna pattern is that the radiation pattern £„(<£) from 
an antenna with a finite aperture d\% completely determined by a series of values spaced 
Kid radians apart, that is, by the sample values E^d), where n is an integer. In 
Fie 7 50a is shown the antenna pattern E(</>) and the sampled points spaced Ijd radians 
apart. The sampled values E s {nXjd), which determine the antenna pattern, are shown 

m The antenna pattern E a (<f>) can be constructed from the sample values £,(«A/<0 with a 
pattern of the form (sin y>)/y about each of the sampled values, where y> = Hrf/A) sin f. 
The (sin y>)/v> function is called the composing function and is the same as that used in 



322 Introduction to Radar Systems [Sec ? g 



antenna pattern is given by 

oo 

E a (4>)= 2 E, 



(nl\ sin |>(rf 
Ad/ -nidi A 



jd/X)(sin 4> - nXld)~\ 



id I X)(sin <f> - nl/d) 



(7.44) 



that is, the antenna pattern from a finite aperture is reconstructed from a sum of ( sin wMw 



*— ^*l_J 




i 
l 
1 






l\ 

i 

i 
i 
i 


1 
1 
1 
1 




1 >. 

! ! 






3X 


2X 
d 


d- 


3 
( 


X 2X 
d d 

i) 


3X 4X 
d d 


5X 


sin # 


1 














E 


s Kn\/d) 


| 




3X 
4 


_2 


X 


l c 


12 


2 


X 


3 


X 4X 
d 


5X 
d 


sin ^ 



(*) 




Fig 7.50 («) Radiation pattern E(</>) with sampled values spaced X/d radians apart where d - 
aperture dimension; (A) sampled values EjinX/d), which specify the antenna pattern K) (cTrecon"- 

Stlern^T" ^ "^ ^ ^ C ° mP ° Sing fUnC "° n '° a PP roxima * the desiS Sdiadon 

The (sin v»)/y composing function is well suited for reconstructing the pattern Its 
value at a particular sample point is unity, but it is zero at all other sample points. In 

dSS;-. S n ^I UnCt J , n Can b£ readil y g enerated with a uniform aperture 
distribution The Woodward-Levinson synthesis technique consists in determining 
the amplitude and phase of the uniform aperture distribution corresponding to each of 
totribulion CS and Perf ° rming a summation t0 obtain the required over-all aperture 

n T £ -T'T l istribution ™y be fou "d by substituting the antenna pattern of Eq. 
(/.44) into the Fourier-transform relationship given by Eq. (7.14). The aperture 



„ nl Antennas 323 

Sec. 7.8] 

distribution becomes «, , ^ i nirnzX / 7 4V > 

^"U-Mvj^l-V) (7 ' 45) 

Therefore the aperture distribution which generates the „th (sin vO/v OTm P 0S jJf 
pattern has uniform amplitude and is proportional to the sampled value E s {nlld) 
The phase across the aperture is such that the individual composing patterns are 
Solaced f'om one another by a half a beamwidth (where the beamwidth is here 
defined as the distance between the two nulls which surround the mam beam) The 
phase is given by the exponential term of Eq. (7.45) and represents a linear phase change 
of nix radians across the aperture. . . ,, . 

The number of samples N needed to approximate the desired antenna pattern £(g is 
determined by the condition that -n\l < <£ < W2, or -1 < sin f < 1. Therefore 
\Nl\d\ < 1 If \N\ > d\K the antenna will have supergain, which is an undesirable 
condition and is to be avoided. 12 *. 1 - Therefore the number of samples required to 
approximate the radiation pattern from a finite aperture of width d is 2d\l 

The essential difference between Fourier-integral synthesis and the Woodward- 
Levinson method is that the former gives a radiation pattern whose mean-square 
deviation from the desired pattern is a minimum, and the Woodward-Levinson method 
gives an antenna radiation pattern which exactly fits the desired pattern at a finite 
number of points. The behavior of the synthesized pattern between the sampled 
points of the Woodward-Levinson method cannot be controlled. Since the Wood- 
ward-Levinson synthesis technique is not based on the Fourier integral, it is not optimum 
in the least-square sense and therefore possesses a greater mean-square error than the 
Fourier synthesis. However, the least-mean-square criterion is not necessarily the 
best in all cases. According to Ruze, 121 it commands no preference on theoretical 

^The^Fourier-integral method is useful when the antenna pattern can be specified 
analytically and when the integrations can be readily performed The Woodward- 
Levinson method is more useful when the pattern to be approximated is of a complicated 
shape and cannot be specified by simple analytical expressions. The flexibility oi the 
latter permits one to "see" the nature of the synthesized pattern even before the aperture 
distribution is computed. If necessary, adjustments can be made to obtain the desired 
balance between the faithfulness with which abrupt changes in the pattern can be 
reproduced and the level of the sidelobe ripples. 

Dolph-Chebyshev Arrays.™'™- 133 The Fourier and Woodward-Levinson tech- 
niquesare but two methods of synthesizing ar arbitrary radiation pattern in an optimum 
manner. There are any number of other criteria which might serve to specify an 
"optimum" method for synthesizing antenna patterns. 

An important synthesis problem in antenna design is to find the aperture distribution 
that produces a radiation pattern with the narrowest beamwidth for a specified sidelobe 
level The solution to this problem was given by Dolph for symmetric broadside 
arrays of equally spaced point sources energized in phase. 128 The optimum aperture 
distribution that minimizes the beamwidth (defined as the distance between the two 
nulls enclosing the main beam) for a given sidelobe level is described in terms of the 
Chebyshev polynomials for the discrete linear array of half-wavelength spacing. Not 
only does the Dolph-Chebyshev distribution yield the minimum beamwidth when the 
sidelobe level is specified, but conversely, it can also be shown to produce the lowest 
sidelobe level when the beamwidth is specified. 

The principle of the Dolph-Chebyshev method will be briefly sketched here The 
details of calculating the required aperture distribution may be found in the litera- 



ture. 129 - 132 



324 Introduction to Radar Systems [Sec 7 g 

Assume that the array consists of an even number of elements 2N. The radiation 
pattern may be found by summing the patterns from elements taken in symmetrica" 
pairs about the center of the array. The radiation pattern is therefore p^Sdto 



E 2x(<t>) = 2~ZA k cos 



i-=i 



(2k 



l)7r — sin 6 

A \ 



(7.46a) 



where A k is the amplitude of the *th element, d e is the element spacing, and the other 
symbol^have been defined previously. If x = CO s {<dJX) In & the ^radiation 

N N 

(7.46b) 



E 2 y(<f>) = 2gA t cos [(2fe - 1) cos" 1 x] = 2%A k T ik - 1 (x) 



*=i 



where T^_ x (x) is the Chebyshev polynomial of degree 2k — 1 133 
polynomial of degree « is defined as 

T n(x) = cos (« cos" 1 x) for |x| < 1 



The Chebyshev 

(7.47) 

Equation (7.46a) may therefore be expressed as a polynomial of degree » and the 
properties of known polynomials may be used to synthesize the pattern Dolph™ 
has shown that when the radiation pattern is equated to a Chebyshev polynomial the 
resultmg pattern is optimum in the sense that the beamwidth is a minimum for a 
specified sidelobe level, or vice versa. The Dolph-Chebyshev radiation pattern is 



E 2n(</>) = T 2N _ 1 (x x) = T 2 



2N-1 



x cos 



d. . 

it — sin 

X 



*). 



(7.48) 



where x is related to r/, the ratio of the main beam to the sidelobe level, by 

ViW = V (7.49) 

E eZ«t g nM )t0 ( l 48 l n" d Substitutin S the definiti ° n ^ the Chebyshev polynomial 
given by (7.47) gives the following: J 



N 



2 2^fcCOS 



(2k- l)7r^sin<£ 



= cos I 



(2N- l)cos" 



x cos { 77 -^ sin <f> 

A 



(7.50) 



Both sides of this equation are polynomials of degree 27V - 1, or one less than the 
number of elements constituting the array. The coefficients A k specify the aperture 
distribution necessary to obtain the optimum radiation pattern and may be found from 
trie above equation. 

It was assumed in the above that there was an even number of elements in the array 
Similar expressions can be derived for the case where the number of elements is odd 

Qualitatively, the characteristics of the optimum Dolph-Chebyshev antenna pattern 
can be seen from an examination of the Chebyshev polynomial. In Fig. 7.51 is shown 
Ux j= 128* -256* + 160* - 32* + 1. It oscillates between the values ±i 
Fa 7 4^ a " d ! nc ; eases monotonically for x > 1. The argument x x is used in 
tq. (7.48) instead of* in order to restrict x to the range -1 < x < 1 required bv its 

detrmnTed bTth" ^ 'T? 1? * ^ aCC ° rdi " 8 * ^ ^th/So^S 
iltTl !? . y ™° not ° mca «y ^creasing portion of the polynomial, while the side 
^bes are determined by the oscillating portion, and the main beam is , times the maxi- 
mum amplitude of the sidelobes. 

hJtl^uT a r! T g ?™ ^ thC Dol P h -Chebyshev distribution is characterized by 
having all its sidelobes of equal magnitude. The aperture distribution, and hence the 
antenna pattern, is completely specified from either the beamwidth or the sidelobe level 
once the number of elements is given. 



Sec. 7.8] 



Antennas 325 



The broadside half-power beamwidth of a Dolph-Chebyshev array of aperture 
dimension ^ given in Fig. 7.52 as a function of sidelobe level. These values are 
vaHd for small beamwidtli { 6 B < 12°).- (The half-power beamwidth of an array 

tolxaminey When , = 1 , the energy across the aperture is concentrated at the edges. 



7-.U) 




Fig. 7.51. Chebyshev polynomial of degree 8. 

The pattern is similar to that produced by a two-element interferometer with spacing d 
All sidelobes are equal to the main beam. (In previous discussions sidelobes which 
were equal in magnitude to the main lobe were called grating lobes) 

The other limiting case occurs when r, = co, that is, when sidelobes do not exist. 
This occurs when the currents on the array elements are proportional to the coefficients 
of a, b in the expansion (a + A)*" 1 , where N is the number of elements m the array. 
For a six-element array the relative amplitudes 
applied to the elements would be proportional 
to 1, 5, 10, 10, 5, 1 . This is called the binomial 
distribution and was first proposed by John 
Stone Stone. 134 It is not often used in practice 
because of its relatively wide beamwidth and 
the large current ratios required across the 
aperture, especially when the number of ele- 
ments is large. The Dolph-Chebyshev dis- 
tribution includes all distributions between the 
binomial and the interferometer, or edge, 
distribution. The uniform distribution, how- 
ever, is not a special case of the Dolph- 
Chebvshev distribution because its sidelobes are not of equal magnitude. 

The uniform sidelobe level produced by the Dolph-Chebyshev array pattern assumes 
an antenna with isotropic elements. If directive elements were used, the over-all 
pattern would be equal to the product of the array pattern and he element pattern. 
In general, the pattern would have decreasing sidelobes. A small reduction in beam- 
width can be obtained by designing the antenna with an array pattern consisting of 
increasing sidelobes so that, when multiplied by the element factor, the resultant 
pattern has uniform sidelobes. 135 



.. 70 A /d 



H 65 \/d - 



! 60A/2 



! 55A/2 



x 50 \/d 




25 30 35 
Side-lobe level, db 



Fig. 7.52. Approximate 
Dolph-Chebyshev arrays. 



beamwidth for 



326 Introduction to Radar Systems 



[Sec. 7.8 



V V 



I 



W V 



thl h X?u lph ' Ch ^ ySheV distribution § ives an optimum one-way pattern in the sense 
that the beamwidth is a minimum for a specified sidelobe level. In radar however it 

of M TZ? P T7 that ? ° n ™P™ tanc *- The two-way pattern for a radar antenna 
of M + 1 elements designed with a Dolph-Chebyshev distribution is (T )* Although 
this is a polynomial of degree 2m, it is not equal to the Chebyshev polynomial of the 
same degree (T 2 J and the two-way pattern does not represent the optimum relation- 
ship between beamwidth and sjdelobe level. Using as a basis the relationship 
T 2m = 2{T m f - 1 = 2(T m + V2/2)(T m - V2/2), Mattingly^ indicates that an opti- 
mum two-way pattern can be achieved with antennas in which slightly different trans- 
mit and receive patterns are obtained using nonreciprocal devices. One example is 

shown in Fig. 7.53. The power divider apportions 
the transmitter power in accordance with T m + a/2/2. 
On reception, the isolator introduces sufficient attenu- 
ation in the reverse direction to correspond to the 
T m — V2/2 distribution. According to Mattingly, 
the extended Chebyshev design will improve the 
beamwidth by about 10 per cent over the conventional 
Chebyshev design. For a given beamwidth, the 
equivalent one-way minor-lobe improvement is 
approximately 4 to 5 db. 

Taylor Distribution. Van der Maas 130 has shown 
that as the number of elements of a Dolph-Chebyshev 
array is increased, the currents in the end elements 
of the array become large compared with the currents 
in the rest of the elements and the radiation pattern 
becomes sensitive to changes in the excitation of the end element. This sets a 
practical upper limit to the number of elements which can be used in a Dolph-Chebyshev 
array and therefore sets a lower limit to the width of the main beam which can be 
achieved in practice. 

In the limit, as the number of elements approaches infinity, the radiation pattern of a 
Dolph-Chebyshev array approaches 



Power divider 



I Duplexer | JReceiv 



|Tron 



ismitter 



Fig. 7.53. Nonreciprocal array with 
two-way Chebyshev pattern. (After 
Mattingly,™ Proc. IRE.) 



E(d)) -. I costt(u 2 - A 2 f 
hW ~ [cosh t^A'-u^ 



A 2 <u 2 
A 2 >u 2 



(7.51) 



where u = (djX) sin <f> 

d = aperture dimension 

<j> = angle measured from normal to array 
cosh -n-A = sidelobe ratio 

The main lobe appears in the region u 2 < A 2 . An infinite number of equal sidelobes 
appears in the region « 2 > A 2 . This ideal radiation pattern is physically unrealizable 
because of the behavior of the radiation pattern in the remote sidelobe region, and the 
corresponding aperture distribution contains infinite peaks at the edges of the antenna 
However, Taylor 137 has shown that design procedures may be obtained for approxi- 
mating the ideal radiation pattern of Eq. (7.51) with a physically realizable aperture 
distribution. The antenna pattern produced by a Taylor distribution has uniform 
sidelobes, just as does the Dolph-Chebyshev pattern, but only in the region of the main 
beam. Unlike the Dolph-Chebyshev pattern, the sidelobes of the Taylor pattern 
decrease outside a specified angular region. The region in which the sidelobe level is 
Hn m ls , defined h y MV sin 0| < n, where n is a finite integer. In the region where 
lid/A) sin <f>\ > n, the sidelobe level decreases with increasing <f>. Hence ±n divides 



Sec. 7.8] Antennas 327 

the radiation pattern into a uniform sidelobe region surrounding the main beam and a 
decaying sidelobe region. 

The Taylor distribution does not produce an optimum pattern as does the Dolph- 
Chebyshev. Its beamwidth will be broader than that of a Dolph-Chebyshev array by 
the factor 



a = 



n (7.52) 



V^ 2 + (n - \) 



The value of n does not have to be very large in order to make a only a few per cent 
greater than unity. For example, if the design sidelobe level is 25 db, a Taylor distri- 
bution with n = 5 gives a beamwidth 7.7 per cent greater than the optimum produced 
by the ideal, but unobtainable, Dolph-Chebyshev distribution. A value of n = 8 
gives a difference in beamwidth of 5.5 per cent. 

The Taylor distribution is specified by two parameters: the design sidelobe level fj 
(ratio of the main beam to the sidelobe level) and n, which defines the boundary between 
the region of uniform sidelobes and decreasing sidelobes. In selecting the integer «, 
it is essential to avoid values that are too small. Taylor states that n must be at least 3 
for a design-sidelobe ratio of 25 db and at least 6 for a design-sidelobe ratio of 40 db. 
The larger n is, the sharper will be the beam. However, if n is too large, the same 
difficulties as arise in a Dolph-Chebyshev distribution will occur. The distributions 
for high values of h are peaked at the center and at the edge of the aperture, while low 
values of n produce distributions which taper from a maximum value at the aperture 
center to a minimum at the edge. 

Care must be exercised in the selection of the sidelobe level of a Taylor or a Dolph- 
Chebyshev distribution. Very large antennas with narrow beamwidths may exhibit a 
severe degradation in gain because of the large energy contained within the sidelobes as 
compared with that within the main beam. This may be avoided by requiring the, 
average sidelobe level to be less than the gain; that is, if 40 db antenna gain is required, 
the average sidelobe level must be less than —40 db. Narrow-beamwidth antennas 
with Taylor distributions can be realized without significant reduction in gain by 
properly choosing the value of n as described by Hansen. 164 

The Taylor distribution has also been applied to synthesizing the pattern of circular, 
two-dimensional apertures. 138-139 

Modified (sin -nu)\-nu Patterns. The radiation-pattern synthesis technique in which 
all the sidelobes are of equal intensity (Dolph-Chebyshev) or of almost equal intensity 
(Taylor) may not always be desirable from an operational point of view. In certain 
radar applications it may be of advantage to have the sidelobe level decay rapidly on 
either side of the main beam. For example, interfering or spurious signals which enter 
the radar receiver via the sidelobes might appear from any angle when the antenna 
pattern contains equal sidelobes. If the antenna sidelobes were \o decrease with 
increasing angle from the main beam, interfering signals would be more likely to cluster 
in the vicinity of the main beam. They would be easier to recognize as false targets 
because of the symmetry of the antenna pattern than if they appeared far removed from 
the main beam. Another example of where an antenna pattern with rapidly decaying 
sidelobes is preferred over an equal-sidelobe pattern is in low-noise applications since 
it is important that the portion of the radiation pattern which illuminates the relatively 
"hot" ground be kept to a minimum. Hence it may be better, in certain instances, to 
sacrifice some beamwidth and low near-in sidelobes for sidelobes which decay rapidly. 

A one-parameter family of line-source distributions suitable for radar applications 
was suggested by Taylor for achieving radiation patterns with a main lobe of adjustable 
amplitude and a sidelobe structure similar to that of a uniformly illuminated aperture. 140 



328 Introduction to Radar Systems 
The radiation pattern is of the form 

" sin tt(u 2 - B 2 f 

£(# = 



tt(u 2 - B 2 f 
sinh tt(B 2 - u 2 f 
tt(B 2 - u 2 f 



B 2 <u l 



B 2 > u 2 



[Sec. 7.8 



(7.53) 



where u = (d/X) sin <f> 

d = aperture size 

B = a parameter which determines level of first (highest) sidelobe 
The region B 2 > u 2 corresponds to the main lobe, and B 2 < u 2 corresponds to the 
sidelobes. If rj is the sidelobe voltage ratio, B is found from the solution of the trans- 
cendental equation 

. ,__ sinh ttB 
V = 4.603 — (7.54) 

The half-power beamwidth /3 , measured in terms of standard beamwidths (a standard 
beamwidth is X/d radians), may be obtained by solving the following transcendental 
equation : 

1 sinh ttB sin n \{BJ2f - B 2 f 
Li2L ^ (7.55) 



V2 ttB *[.Wf - B 2 f 

The aperture distribution corresponding to the modified pattern of Eq. (7.53) is 

277 



A(z) 



N>-$ 



JqMttB 



(7.56) 



where J is a Bessel function of the first kind and z varies from —d/2 to + d/2. The 
aperture distribution is concave, uniform, or convex, depending upon whether B 2 is less 
than, equal to, or greater than zero, respectively. 
The gain of this antenna pattern is given by 



G = 



Ad sinh 2 ttB 



where 



ttBaI (2ttB) 
c _ 4dsin 2 (i7rB) 
~ irBXJ {i2irB) 

Ux) = ]Io(t) dt 
Jo 



Breal 



B imaginary 



(7.57a) 

(7.57b) 



Jo 



Mx) = J U) dt 



and I (x) is the modified Bessel function of zero order. 

Table 7.2 lists some of the important properties of this type of radiation pattern. 

Table 7.2. Properties of the Modified (sin mi)lnu Radiation PatternI 



Sidelobe 


B 2 


Beamwidth, 


Ratio of beamwidth 


Aperture efficiency, 


ratio, db 




deg 


to ideal beamwidth 


per cent 


10 


-0.2113 


46M/d 


1.156 


96.4 


15 


0.1266 


52M/d 


1.151 


99.3 


20 


0.5455 


58.7A/rf 


1.146 


93.3 


25 


1.0464 


63.9AM 


1.141 


86.3 


30 


1.6286 


6S.U/d 


1.136 


80.1 


35 


2.2911 


11. 2X1 d 


1.131 


75.1 


40 


3.0328 


HAUd 


1.125 


70.9 



t Extracted from Taylor, 110 courtesy Hughes Aircraft Co. 



§ EC 7 91 Antennas 329 

The "ideal beamwidth" referred to in the fourth column is that of a radiation pattern of 
the form cos Wu 2 — A*, in which the sidelobes are of uniform amplitude. The ratio 
of beamwidths in column 4 compares directly with the a of Eq. (7.52). The efficiency 
given in the last column is the ratio of the gain of the modified (sin -nu)\-nu radiation 
pattern to the gain of an antenna with uniform aperture illumination. 

7.9. Cosecant-squared Antenna Pattern 

It was shown in Sec. 2.1 1 that a search radar with an antenna pattern proportional to 
esc 2 6, where d is the elevation angle, produces a constant echo-signal power for a 



Parabolic 
reflector 



Displaced 
from original 
parabolic 
contour 




Fig. 7.54. Cosecant-squared antenna produced by displacing the reflector surface from the original 
parabolic shape. 

target flying at constant altitude, if certain assumptions are satisfied. Fan-beam 
search radars generally employ this type of pattern. 

Antenna Design. The design of a cosecant-squared antenna pattern is an application 
of the synthesis techniques discussed in the preceding section. Examples of cosecant- 
squared-pattern synthesis are given in the literature. 5 - 121 ' 124 ' 141 ' 142 

The cosecant-squared pattern may be approximated with a reflector antenna by 
shaping the surface or by using more than one feed. The pattern produced in this 
manner may not be as accurate as might be produced by a well-designed array antenna, 
but operationally, it is not necessary to approximate the cosecant-squared pattern very 
precisely. A common method of producing the cosecant-squared pattern is shown in 
Fig. 7.54. The upper half of the reflector is a parabola and reflects energy from the 
feed in a direction parallel to the axis, as in any other parabolic antenna. The lower 
half, however, is distorted from the parabolic contour so as to direct a portion of the 
energy in the upward direction. A spoiler plate is sometimes used to give a cosecant- 
squared pattern (Fig. 1.10). 

A cosecant-squared antenna pattern can also be produced by feeding the parabolic 
reflector with two or more horns or with a linear array. If the horns are spaced and fed 
properly the combination of the secondary beams will give a smooth cosecant-squared 
pattern over some range of angle. 1 - 143 - 144 A reasonable approximation to the cosecant- 
squared pattern can be obtained with but two horns. A single horn, combined with a 
properly located ground plane, can also generate a cosecant-squared pattern with a 
parabolic reflector. 145 The feed horn, plus its image in the ground plane, has the same 
effect as two horns. 



330 



Introduction to Radar Systems 



[Sec. 7.10 



The traveling-wave slot antenna 146 and the surface-wave antenna 147 can also be de- 
signed to produce a cosecant-squared antenna pattern. 

Loss in Gain. An antenna with a cosecant-squared pattern will have less gain than a 
normal fan-beam pattern generated from the same aperture. To obtain an approximate 
estimate of the loss in gain incurred by beam shaping, the idealized patterns in Fig. 7.55 
will be assumed. The normal antenna pattern is depicted in Fig. 7.55a as a square beam 
extending from 6 = to 6 = radians. The cosecant-squared pattern in Fig. 7.556 




(a) 

Fig. 7.55. Idealized antenna patterns assumed in the computation of the loss in gain incurred 
with a cosecant-squared antenna pattern, (a) Normal antenna pattern; (6) cosecant-squared 
pattern. 



is shown as a uniform beam over the range < < 6 and decreases as esc 2 0/csc 2 6 
over the range 6 < 8 < 6 m . The gain G of the square beam in Fig. 7.55a divided by 
the gain G c of the cosecant-squared antenna beam in Fig. 7.556 is 



G 
G c 

For small values of O , 



esc 



i re m 

±— csc 2 0o~0 

r0 n Je 



o + sin 2 fl (cot d — cot 6 m ) 
n 



— *** 2 — 6 cot 0„ 
G, 



(7.58) 



(7.59) 



where all angles in the above formulas are measured in radians. For example, if 
6 = 6° and 6 m = 20°, the gain is reduced by 2.2 db compared with a fan beam 6° wide. 
If m is made 40°, the loss is 2.75 db. In the limit of large 6 m and small 6 , the loss 
approaches a maximum of 3 db. 

7.10. Effect of Broadband Signals on Antenna Patterns 

The Fourier-integral-transform relationship between the radiation pattern E(<j>) and 
the aperture distribution A(z) as expressed in Eqs. (7.1 1) and (7.14) of Sec. 7.2 applies 
only when the signal is a CW sine wave. The spectrum of a sine wave of frequency^ is 
a single delta function at/ =f . If the signal were a pulse or some other radar wave- 
form with a spectrum of noninfinitesimal width, the simple Fourier integral which 
applies to a CW sine wave would not give the correct radiation pattern nor would it 
predict the transient behavior. In most cases of practical interest the spectral width of 
the signal is relatively small, with the consequence that the pattern is not affected 
appreciably and the Fourier-integral relationships are satisfactory approximations. 
However, when the reciprocal of the signal bandwidth is comparable with the time 
taken by a radar wave to transverse the antenna aperture, bandwidth effects can be 
important and signal distortion may result. 



Sec. 7.10] Antennas 331 

Broadband Radiation Pattern. The radiation pattern produced by a CW sine wave 
of frequency /„ is « a/2 , f \ 

E(<f>) = A(z) exp j2if^ z sin ^ dz (7.60) 

J -a/2 \ C I 

where a = aperture dimension 

c = velocity of propagation 

(/> = angle measured from perpendicular of antenna 
This expression is the same as Eq. (7. 10) except that the wavelength X is replaced by its 
equal c// . The aperture distribution A(z) is the inverse Fourier transform, or 

A{z) =■& | £(</>) exp l—j2ir& z sin <f>) d(sin <f>) (7.61) 

C J-x \ C I 

Equations (7.60) and (7.61) apply for a fixed frequency f . Radar signals, in general, 
are not of fixed frequency but are characterized by finite spectral width. Letting 
u = sin </>, the antenna radiation pattern as a function of frequency may be written as 

£(/,„) = f a/2 A(z) exp J ^^ dz (7.62) 

J -a/2 C 

and the equivalent aperture distribution is 

A(z) = - f °° E(f,u) exp (- &^B\ du (7.63) 

If the spectral distribution of the signal is 5(/), the resultant antenna pattern will be -a 
weighted sum of E(f,u), with the weight function S(f). The effective broadband 
antenna pattern is therefore given by 

E f (u) =js(f)E(f,u) df (7 Ma) 

E f (u) = J J S(f)A(z) exp J2%!Z!t dz df {1Mb) 

EXu)=jyj , s(D4(z)exp _;2t7/(c-^) dzdt,df (7.64c) 

where s(£) = ^(0, the signal waveform, is the inverse Fourier transform of S(f). The 
above three equations determine the resultant effective antenna pattern when the 
signal occupies a significant bandwidth. 

The frequency spectrum S(f) applies to that of the transmitted signal or to the 
received signal at the antenna terminals. If matched filters (Sec. 9.2) are employed at 
each element on reception, the frequency-response function of each filter is the complex 
conjugate of the spectrum S(f) and is denoted S*(f). The output of the matched 
filter is therefore S(f)S*(f) = \S(f)\ 2 = G(f), where G(f) is the power-density spec- 
trum of the transmitted waveform. When matched filters are employed, G(f) should 
be substituted for S(f) in the equations given above. 

As an example of the effect of bandwidth on the antenna pattern, consider an aperture 
with a uniform distribution and a signal with a constant spectral distribution, so that 
A{z) = l/afor-o/2 < z < a/2 and S(f) = 1 /(/ 2 - /J for/i </</ 2 . Theradiation 
pattern as function of frequency is 

w /■ \ f " /2 1 j2irfzu , sin (Trfau/c) ,_ „. 

£(/,«) = - e x P — J — d2 = \ , ( 7 - 65 ) 

J -o/2 a c TTjaujc 



332 Introduction to Radar Systems 
Integrating over the frequency band of S(f) gives 

1 



[Sec. 7.10 






sin {irfaujc) = Si (irf 2 aulc) - Si (nfau/c) 

A ~ A -nfaulc 7r(f 2 - fjau/c 



(7.66) 



where Si (x) is the sine integral function of x defined by the integral | [(sin s)/s] ds. In 

the limit as f x -»/ 2 , it can be shown that Eq. (7.66) approaches the expression 
[sin {Trf aulc)]l{Trf Q aujc), where/ = (f } + / 2 )/2, which is the same as would be produced 
by a CW sine wave and a uniformly illuminated aperture. If the spectrum extended 
from/ = to f=f 2 (that is,/i = 0), the radiation pattern would be of the form of 
[Si {jrf 2 aulc)\l{nf 2 aulc). This should be compared with the radiation pattern produced 




Fig. 7.56. Radiation patterns for a uniformly illuminated aperture with CW sine wave of frequency /, 
[(sin x)/x curve] and with a broadband signal with uniform frequency spectrum over the range to f, 
[(Si x)/x curve], where x = Trf 2 au/c. 

by a CW sine wave of frequency /=/ 2 from the same aperture, which is 
[sin (TTf 2 aulc)]](Trf 2 auJc). A comparison of these two functions is shown in Fig. 7.56. 
The beam of the wide-spectrum pattern is broadened, the sidelobe radiation is raised, 
and the lobe structure essentially disappears. Figure 7.56 indicates that the frequency 
f 2 must be of the order of twice the frequency / of the CW sine wave in order for the 
broadband-pattern beam width to be narrower than the CW pattern beamwidth. 

Consider next a linear array of N elements (N even) spaced a distance d e apart. The 
radiation pattern may be expressed as 

£(/>«) = 2 cos " U_jl- ( 7 67 ) 

71 = 1 C 

The transmitted signal is assumed to consist of a discrete number A: of sine waves with 
harmonically related frequencies, or 



S(/) = 2<5(/-fc/o) 



fc=i 



(7.68) 



Substituting Eqs. (7.67) and (7.68) into (7.64a) gives 



E f {u) 



J k=l 



*/- 



kf/icos ^-^^ df-. 



= | f cos (2n - Dknf d e u (?69) 

k= ] «=1 C 



The more frequencies used, the fewer the number of elements required. In principle, 
the number of elements 7Y in the array can be traded for the number of harmonically 
related frequencies K and still retain the same "effective" radiation pattern. This is 
sometimes called space frequency equivalence. U& - 19S A similar relation holds for N odd . 



Sec. 7.10] 



Antennas 333 



As an example of the application of space frequency equivalence for an odd number 
of elements, consider an 11 -element linear array with spacing d t operating at a fre- 
quency f . This array may be replaced by a three-element linear array with the 
same spacing between elements but with the center element at a frequency /„ and both 
the outer elements radiating at frequencies f , 2/ , 3/ , 4/ , and 5/ . 









A 


/) 








U) 








1/a 










-a 


>Z 





a 


>Z 


'- 






S[f) 






[6) 






1 
f z -f, 








1 


1 





-fo - f i 



fy f f Z f^. 



4></> 




Fig 7 57 Illustration of the effect of wide-bandwidth signals on the equivalent aperture distribution. 
(a) The actual distribution A(z); (b) the signal frequency spectrum 5(/); (c] ) the equiva lent single- 
frequency aperture distribution required to give the same pattern as the combination of (a) and (b). 
{After Damin, Niebuhr, and Nilsson™ IRE WESCON Conv. Record.) 

It may be shown 149 that the radiation pattern of an antenna radiating a wideband 
signal may be generated by a single-frequency CW sine wave of frequency f if the 
distribution across the antenna aperture is given by 

A (y) =\ f jS(f)A(!f) d/ = /o Ji A(z) S (^) dz (7.70) 

With a matched filter S(f) must be replaced by G(f). The equivalent single frequency 
aperture distribution may not always be physically realizable. The equivalent single- 
frequency aperture distribution for a uniform distribution and a uniform frequency 
spectrum [equivalent radiation pattern given by Eq. (7.66)] is 



A (y) 



fo In (/ 2 //i) 
a fz—fi 
f a In (/.a/2/,j») 
a f 2 ~fi 





for \y\ < 



(/i//o)« 



f OT (Ji!m<\y\< 

2 



2 



(7.71) 



for \y\ > 



iklfo)a 



The functions A{x), S(f), and A (y) for this example are shown in Fig. 7.57. When 
f % =/„ and/! = 0, corresponding to the example of Fig. 7.56, the equivalent aperture 



334 Introduction to Radar Systems 



[Sec. 7.10 
This distribution becomes 



distribution is A^iy) = (l/«) In (a/2y) for < \y\ < a/2, 
infinite at y = 0. 

The frequency domain may be used to resolve the grating-lobe ambiguities produced 
by a widely spaced array antenna. The positions of the grating lobes are a function of 
frequency, but the position of the main beam remains fixed, assuming a frequency- 
independent array. Targets which appear on the grating lobes will give different 
apparent angle readings with different frequencies. This characteristic may be used to 
resolve the grating-lobe ambiguities in a manner quite analogous to that in which 

multiple-repetition frequencies may resolve 
ambiguities caused by multiple-time-around 
echoes. 194 

The broadband radiation pattern of Eq. (7.64) 
assumes that the receiving device is capable of 
adding the. radiated field strengt